The probability that both events A and B will occur is 0.56
Step-by-step explanation:
It is given that,
- There are 9 pieces of chocolate, 7 fruit chews, 9 lollipops, and 9 peppermints in a bowl.
- The total number of pieces in the bowl = 9+7+9+9 = 34 pieces.
- A girl and a boy each randomly grab a piece of candy from a bowl.
Therefore, two events A and B will occur.
Event A ⇒ A girl grabs a lollipop :
P (to grab lollipop) = No.of lollipops / Total pieces
We know that, no.of lollipops = 9 and the total pieces = 34
P (to grab lollipop) = 9 / 34.
Event B ⇒ A boy grabs a fruit chew :
P (to grab fruit chew) = No.of fruit chews / Total pieces in bowl after event A.
We know that, no.of fruit chews = 7 and the total pieces in the bowl after grabbing one lollipop is 33 pieces.
P (to grab fruit chew) = 7 / 33
Probability that both events A and B will occur :
P (event A and B) = P (to grab lollipop) × P (to grab fruit chew)
⇒ 9/34 × 7/33
⇒ 63/1122
⇒ 21/374
⇒ 0.56
The probability that both events A and B will occur is 0.56