Question

A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?

Answer 1

Answer:
`(5)/(91)`

Explanation:

Given: Number of peach in basket = 5

Number of oranges = 2

Total fruits in basket = 3+2+2+2+5=14

The probability that Jack picks a peach is given by :-

`\text{P(peach)}=(5)/(14)`

Now, the total fruit remains in the basket = 14-1=13

The probability that Bethany picks an orange after Jack has picked a peach is given by :-

`\text{P(orange)}=(2)/(13)`

Thus, the probability that Jack gets a peach and Bethany gets an orange is given by :-

`\text{P(peach)}*\text{P(orange)}=(5)/(14)*(2)/(13)=(5)/(91)`

Answer 2

3 + 2 + 2 + 2 + 5 = 14 total fruits

P(jack gets peach) = 5/14
not replaced
P(bethany gets orange) = 2/13

P(both) = 5/14 * 2/13 = 5/91 <===