Question

A basket contains 13 pieces of fruit: 5 apples, 5 oranges, and 3 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?
A.25/156
B.10/13
C.25/169
D.5/6

Answer 1

Use formula for theoretical probability:

$Pr=\dfrac{\text{the number of favorable outcomes}}{\text{the number of possible outcomes}}.$

1. The probability that Jonas will get an orange is

$Pr(\text{Jonas gets orange})=\dfrac{5}{13}.$

2. Ben is taking a piece second and he has 12 piecies left, among them 5 apples, 4 oranges and 3 bananas. The probability that Ben will get an apple is

$Pr(\text{Ben gets apple})=\dfrac{5}{12}.$

3. Use the product rule to determine

$Pr(\text{Jonas gets orange and Ben gets apple})=\dfrac{5}{13}\cdot \dfrac{5}{12}=\dfrac{25}{156}.$

Answer: correct choice is A.

Answer 2

Probability Jonas gets an orange.
5/13
Probability Beth gets an apple (assuming the previous)
5/12
Probability of both:
25/156