Question

PLEASE HELP! A basket contains four apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. The first time, you get an apple. Then second and third times, you get peaches. Find the probability of this occurring.

A. 25546
B. 100729
C. 132
D. 8125

Answer 1

• 100 / 729

Explanation:

The general formula to calculate the probability of each event is:

• Probability = number of positive (desired) outcomes / number of total outcomes

Number of apples = 4

Number of peaches = 5

Number of fruits = 9

Since the three times you return the radomly selected fruit, and then mix it, the three times the probability is not affected by the previous selection; so, these are independent events, and you can calculate the probability of the joint event as the product of the probabilities of each individual event.

• First time:

Probability of getting an apple = number of apples / number of fruits = 4 / 9

• Second time:

Probability of getting a peach = number of peaches / number of fruits = 5 / 9

• Third time:

Probability of getting a peach = number of peaches / number of fruits = 5 /9

• Joint probability:

= (4/9) × (5/9) × (5/9) = (4 × 5 × 5) / (9 × 9 × 9) = 100 / 729