Theoretical and experimental probability for predictions

 

 

Using theoretical and experimental probability for predictions
a. Jill has a bag of 48 marbles. The probability of pulling out a yellow marble is 5/6. How
many yellow marbles are in the bag?
𝑦𝑒𝑙𝑙𝑜𝑤
𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 ∙ =
𝑦𝑒𝑙𝑙𝑜𝑤
𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑟𝑏𝑙𝑒𝑠
b. Ivan’s batting average is 0.3. If he is up to bat 70 times, how many times can the coach
expect him to hit the ball?
ℎ𝑖𝑡𝑠
𝑎𝑡 𝑏𝑎𝑡 ∙ =
ℎ𝑖𝑡𝑠
𝑎𝑡 𝑏𝑎𝑡
c. The spinner lands on red 5/8 times. How many times can we expect the spinner to land
on red if the spinner is spun 96 times?
𝑟𝑒𝑑
𝑡𝑖𝑚𝑒𝑠
∙ =
𝑟𝑒𝑑
𝑡𝑖𝑚𝑒𝑠
d. A bag holds red, white, and blue marbles. Alison pulls one marble from the bag and
records the results. Then she returns the marble to the bag and pulls another. The table
shows her results.
Color Outcomes
Red 22
White 48
Blue 30
Based on the outcomes, enter the number of times Alison can expect to pull a white
marble if Allison pulls out a marble 25 times.
𝑤ℎ𝑖𝑡𝑒
𝑡𝑟𝑖𝑎𝑙𝑠 ∙ =
𝑤ℎ𝑖𝑡𝑒
𝑡𝑟𝑖𝑎𝑙𝑠
e. It rains 2 out of 12 days in March. If the trend continues, how many days will it rain in
April. April has 30 days.

𝑟𝑎𝑖𝑛
𝑑𝑎𝑦𝑠
𝑟𝑎𝑖𝑛
𝑑𝑎𝑦𝑠 ∙ =
𝑤ℎ𝑖𝑡𝑒
𝑡𝑟𝑖𝑎𝑙𝑠
Part 2: Law of Large Numbers
a. Multiple Choice: The theoretical probability of a coin landing heads up is 1
2
. She flips a fair
coin 4 times, but it lands facing up tails up 3 𝑜𝑢𝑡 𝑜𝑓 4 𝑡𝑖𝑚𝑒𝑠. Which statements best explains
why the theoretical probability is different than her experimental probability?
A. They most likely differ because of the kind of coin is used.
B. They most likely differ because the coin had tails on both sides.
C. They most likely differ because 1
2
𝑎𝑛𝑑 3
4
have different denominators.
D. They most likely differ because the sample size is too small.
b. Multiple Choice: The theoretical probability of rolling a 5 on a 6-sided dice is 1
6
. She rolls the
dice 4 times, but it lands on “5” 2 out of 4 times. Which statements best explains why the
theoretical probability is different than her experimental probability?
A. They most likely differ because 1
6
𝑎𝑛𝑑 2
4
have different denominators.
B. They most likely because of the kind of dice is used.
C. They most likely differ because the dice had “5” on 3 sides.
D. They most likely differ because the sample size is too small