Simple Probability Worksheets.doc

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Simple Probability Worksheets

.

A football manufacturer checks 400 footballs and finds that 8 balls are defective. Find

the probability that the ball chosen is a defective ball.

a. 2%

b. 3%

c. 20%

d. 41%

Solution:

Number of favorable outcomes = Number of defective balls = 8

Number of possible outcomes = Total number of footballs = 400

= 0.02 x 100 = 2%

P(defective football) = number of defective balls / total number of balls = 8 / 400 = 0.02

[Substitute and simplify.]

[Multiply by 100 to write the decimal in percent form.]

The probability that the ball chosen is a defective ball is 2%.

2.

A basketball player attempts 50 baskets and makes 5. What is the probability of the

player making a basket?

a. 0.25

b. 0.1

c. 0.05

d. 0.4




Solution:

Number of favorable outcomes = number of baskets the player makes = 5

Number of possible outcomes = total number of attempts = 50

P(making a basket) = number of baskets / total number of attempts = 5 / 50 = 0.1


The probability of the player making a basket is 0.1.

3.

What are the odds in favor of the coin falling in the shaded region?

a. 1 : 2

b. 1 : 3

c. 1: 1

d. 1 : 4

Solution:

Odds in favor of an event = number of favorable outcomes / number of unfavorable

outcomes.

Number of favorable outcomes = 4

Number of unfavorable outcomes = 4




Odds in favor of the coin falling in the shaded region = 4 / 4 = 1 : 1

4.

The probabilities of John or Paula winning a game are shown in the pie chart. Is this

a fair game?

a. Unfair

b. Fair

Solution:

P (John winning the game) = 0.6

P (Paula winning the game) = 0.4

Each player has different probability of winning the game.

So, the game is unfair game.

5.

Find P(not red), if P(red) is 31%.

a. 31%

b. 19%




c. 69%

Solution:P (red) = 31% = 0.31

[Convert the percent to decimal by dividing with 100.]

= 1 - 0.31 = 0.69

P (not red) = 1 - P(red)

[Probability of an event not happening = 1 - probability of the event happening.]

So, P(not red) is 69%.

[Convert the decimal to percent by multiplying with 100.]

6.

What is the probability of not getting the newspaper on time, if the probability of

getting it on time is 42.4%?

a. 56.1

b. 61.1

c. 59.1

d. 57.6

Solution:

P(on time) = 42.4% = 0.424

P(not on time) = 1 - 0.424 = 0.576

[Subtract]

There is 57.6% chance of not getting the newspaper on time.

7.




The letters C, O, M, P, E, T, I, T, I, O, N are written on cards and put in a hat. One card

is selected at random. What is the probability that the card selected bears a

consonant?

a. 411

b. 511

c. 611

d. 211

Solution:There are six cards on which consonants ('C', 'M', 'P', 'T', 'N') are written.

Number of favorable outcomes = Number of cards having consonants = 6

Number of possible outcomes = Total number of cards = 11

Probability of drawing a card having consonant = Number of favorable outcomes / number

of possible outcomes = 6 / 11

8.

Olga has 8 dollars, 6 nickels, and 10 dimes in her purse. What is the probability of

selecting a dime from her purse?

a. 1011

b. 124

c. 512

d. 114




Solution:

Number of favorable outcomes = Number of dimes = 10

Number of possible outcomes = Total number of coins = 24

= 512

P(dime) = number of dimes / total number of coins = 10 / 24

Probability of selecting a dime is 5 / 12.

9.

20 out of 70 plants had black colored flowers and 50 had violet colored flowers. Find

the probability that a plant had violet colored flowers.

a. 17

b. 57

c. 45

d. None of the above

Solution:

Number of favorable outcomes = Number of plants with violet colored flowers = 50

Number of possible outcomes = Total number of plants = 70

= 57

P(violet) = number of plants with violet colored flowers / total number of plants = 50 / 70

[Simplify.]

The probability that the plant had violet colored flowers is 5 / 7.

10.

A bag contains 15 yellow marbles, 5 black marbles and 15 red marbles. What are the

odds in favor of selecting a black marble?




a. 130

b. 15

c. 16

d. 27

Solution:

Number of favorable outcomes = Number of black marbles = 5

Number of unfavorable outcomes = Number of marbles excluding black = 30

Odds in favor of an event

=Number of favorable outcomesNumber of unfavorable outcomes= 5 / 30 = 1 / 6

Odds in favor of selecting a black marble is 1 /6 .

Solution:Number of favorable outcomes = Number of classes Jerald attended = 9.

Number of possible outcomes = Total number of classes = 11.

P(Jerald attending the class) = number of classes Jerald attended / total number of classes

= 9 / 11

Probability of Jerald attending the class is 9 /11.

12.




What is the probability of getting a number divisible by 2 when the spinner is turned?

a. 25%

b. 12.5%

c. 37.5%

d. 50%

Solution:

The numbers divisible by 2 in the spinner are 2, 4, 6 and 8.


[Since there are 4 numbers divisible by 2.]

Number of possible outcomes = 8

[Since there are 8 sections in the spinner.]

P(number divisible by 2) = Number of favorable outcomes / Number of possible outcomes

= 48 = 0.5 = 50%


So, the probability of getting a number divisible by 2 is 50%.

13.




What are the odds in favor of spinning yellow in the figure?

a. 1 : 2

b. 1 : 4

c. 3 : 4

d. 1 : 1

Solution:

The odds in favor of an event

=Number of favorable outcomes Number of unfavorable outcomes


[Since there are 4 yellow colored sections in the spinner.]

Number of unfavorable outcomes = 4

[Since there are 4 sections colored other than yellow in the spinner.]

Odds in favor of spinning yellow = 4 / 4 = 1 : 1


So, the odds in favor of spinning yellow is 1 : 1.

14.

A number is selected at random from 1 to 16. What is the probability that it is a prime

number?

a. 12

b. 116




c. 16

d. 38

Solution:

The prime numbers between 1 and 16 are 2, 3, 5, 7, 11 and 13.

So, the number of favorable outcomes is 6.

As there are 16 numbers from 1 to 16, the number of possible outcomes is 16.

P(prime number) = (number of favorable outcomes) / (total number of possible outcomes)

= 616 = 38


The probability that a number selected between 1 and 16 is a prime number is 3 / 8.

15.

Cards numbered 1 through 25 are put in a hat. A card is picked up at random. What is

the probability that it bears a number, which is a multiple of 5?

a. 25

b. 34

c. 15

d. 14

Solution:

Number of favorable outcomes = number of multiples of 5 = 5

Total number of possible outcomes = numbers from 1 through 25 = 25




P(multiples of 5) = (number of favorable outcomes) / (total number of possible outcomes)

= 525 = 15


Probability that the card picked up bears a number, which is a multiple of 5 is 1 / 5.

16.

The lettersM, A, T andH are written on cards and put in a bag. What is the

probability that a card drawn from the bag bears the letter 'T ' on it?

a. 33%

b. 50%

c. 25%

d. 75%

Solution:

Number of favorable outcomes = Number of cards bearing the letter 'T' = 1

Number of possible outcomes = Total number of cards = 4

Probability(card with letter 'T') = Number of favorable outcomes / Total number of possible

outcomes = 1 / 4 = 0.25 = 25%

[Simplify the fraction 1 / 4 into decimal.]

The probability that a card drawn from the bag bears the letter 'T' is 25%.

17.




What is the probability of rolling a sum greater than 10 with two number cubes?

a. 14

b. 112

c. 16

d. 512

Solution:

A sum greater than 10 is obtained when the numbers rolled are (5, 6), (6, 5) or (6, 6).


Total number of possible outcomes = 6 x 6 = 36

[Since there are 6 sides in each number cube.]

P(sum greater than 10) = Number of favorable outcomes / Number of possible outcomes

= 336 = 112


The probability of rolling a sum greater than 10 with two number cubes is 1 / 12.

18.

There are 7 blackberries, 6 pears and 4 grapes in a bag. If Gary picks up a fruit at

random from the bag, then what is the probability of the fruit being a grape?

a. 417

b. 617

c. 717

d. 418




Solution:

Number of favorable outcomes = Number of grapes = 4

Number of possible outcomes = Total number of fruits = 17

Probability (grape) = Number of favorable outcomes / Total number of possible outcomes

= Number of grapes / Total number of fruits = 4/ 17

Probability of the fruit being a grape is 4 / 17.

19.

When two number cubes are rolled, what is the probability of getting 11 as the

product of the two numbers?

a. 536

b. 19

c. 111

Solution:

As 11 is a prime number, it has no factors except 1 and itself.

So, the event of getting 11 as product of the numbers rolled with two number cubes is

impossible.

The probability of an impossible event is 0.

So, the probability of getting 11 as the product of the numbers rolled with two number cubes

is 0.

20.




Jake watches his favorite movie channel X every night. The probability that his

favorite movie will be played is 18. What is the probability that his favorite movie will

not be played?

a. 17

b. 18

c. 78

d. None of the above

Solution:P(favorite movie not played) = 1 - P(favorite movie played)

P(favorite movie being played) = 1 / 8

P(favorite movie not played) = 1 - 1 / 8 = 7 / 8

[Substitute and subtract.]

Probability that Jake's favorite movie will not be played is 7 / 8 .

21.

What is the probability of drawing either of the two cards from a deck of playing

cards?

a. 152

b. 126

c. 12




d. 226

Solution:P(club 7) = 1 / 52

[Since there is only one club 7 in a deck of 52 playing cards.]

P(diamond 7) = 1 / 52

[Since there is only one diamond 7 in a deck of 52 playing cards.]

P(club 7 or diamond 7) = P(club 7) + P(diamond 7)

= 152 + 152 = 252 = 126


Probability of drawing either a club 7 or a diamond 7 is 1 / 26.

22.

What is the probability of choosing a vowel in the word REPITITION?

a. 12

b. 15

c. 25

d. 35

Solution:

Number of favorable outcomes = number of vowels in the word = 5

Total number of possible outcomes = total number of letters in the word = 10

P(vowel) = (number of favorable outcomes) / (total number of possible outcomes)

= 510 = 12





Probability of choosing a vowel from the word REPITITION is 1 / 2.

23.

Assuming that a coin dropped from a height will land on any one of the 16 cells, what

is the probability that the coin tossed will land on the region, which is not shaded?

a. 34

b. 112

c. 13

d. 14

Solution:

Number of favorable outcomes = Number of cells not shaded = 12

Total number of possible outcomes = Total number of cells = 16

Probability(coin landing on the region not shaded) = Number of favorable outcomes/Number

of possible outcomes = 12 /16 = 3 / 4

[Simplify the fraction.]

Probability that the coin tossed will land on the region which is not shaded is 3 / 4.

24.




What is the probability of choosing a multiple of 3 from the numbers 1 to 50?

a. 15

b. 825

c. 25

d. 925

Solution:

Number of favorable outcomes = Number of multiples of 3 in the range 1-50 = 16

[Since there are 16 numbers, which are the multiples of 3 : 3, 6, 9, 12, 15, 18, 21, 24, 27,30, 33, 36, 39, 42, 45, 48.]

Number of possible outcomes = Total number of numbers = 50

[Since there are 50 numbers in the range 1-50.]

P(multiple of 3) = Number of favorable outcomes / Number of possible outcomes

= 1650 = 825


The probability of choosing a multiple of 3 in the range 1-50 is 8 / 25.

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