1. What’s the probability that the spinner will land on blue? 2. Samuel has a bowl of fruit containing 3 apples, 2 oranges and 5 pears. If he randomly.

Bell Work1. What’s the probability that the spinner will land on blue?

2. Samuel has a bowl of fruit containing 3 apples, 2 oranges and 5 pears. If he randomly picks 1 piece of fruit from the bowl, what is the probability it will be a pear or an apple?

12 3

45

678

Answers

1.

2.

Different Types of Probabilities

Theoretical vs. Experimental ProbabilityTheoretical Probability:- It is how a probability of an event “should”

happen. Experimental Probability:- Experimental probability refers to the probability

of an event occurring when an experiment was conducted.

Theoretical Probability

There is a bag of blue, green and red chips. There is a 12% possibility of randomly picking a blue chip and a 25% chance of randomly picking a red chip. What is the probability of picking a green chip?

Hint: Your three options are green, blue and red. Their probability will add up to 100%

Answer: 63%

Experimental Probability

P(event) = number of times event occurs total number of trialsYou tossed a coin 10 times and recorded heads 3 times

and tails 7 times.

P(head)= 3/10 , 0.3 or 30%A head shows up 3 times out of 10 trials, P(tail) = 7/10, 0.7 or 70%A tail shows up 7 times out of 10 trials

HEADS

TAILS

Comparing Experimental and Theoretical Probability

Both probabilities are ratios that compare the number of favorable outcomes to the total number of possible outcomes

P(head)= 3/10 or 30%P(tail) = 7/10 or 70%

P(head) = 1/2 or 50%P(tail) = 1/2 or 50%

All results will add up to 100% every time!

Equally Likely OutcomesWhen all the possible outcomes of an experiment are equally likely, the probability of each outcome is:

You’re playing a board game with your family and need to role a 6 to win. If you roll one die, what is the likelihood you’ll roll a 6?

𝑷 (𝐨𝐮𝐭𝐜𝐨𝐦𝐞 )= 𝟏𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐩𝐨𝐬𝐬𝐢𝐛𝐥𝐞𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬

𝐍𝐮𝐦𝐛𝐞𝐫𝐨𝐟 𝐏𝐨𝐬𝐬𝐢𝐛𝐥𝐞𝐎𝐮𝐭𝐜𝐨𝐦𝐞𝐬 = 6

𝑷 (𝐫𝐨𝐥𝐥𝐢𝐧𝐠𝐚𝟔 )=𝟏𝟔

Not Equally Likely Outcomes

If the outcomes are not known to be equally likely, the formula for the probability of an event can’t necessarily be used.

Rick, is concerned about his diet. On any given day, he eats , , , , or servings of fruit and 𝟎 𝟏 𝟐 𝟑 𝟒vegetables. The probabilities are given in the table below.

On a given day, find the probability that Rick eats:

a. Two servings of fruit and vegetables.

b. More than two servings of fruit and vegetables.

c. At least two servings of fruit and vegetables.

Number of Servings

Probability

0.28

0.39 + 0.12 =

0.28 + 0.39 + 0.12 =

0.51

0.79

Jon spins the spinner below 20 times and gets the following results:

1. What is the theoretical probability of spinning each letter?

2. What is the experimental probability of spinning each letter?

3. According to the results, which section is closest to it’s theoretical probability?

A

C

B

BA

Letter #A 7

B 9

C 4

Spinning a “C”

A- 2/5 B- 2/5 C- 1/5

A- 7/20 B- 9/20 C- 4/20

Practice!