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: $\frac{5}{91}$

Step-by-step 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 :-

$\text{P(peach)}=\frac{5}{14}$

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 :-

$\text{P(orange)}=\frac{2}{13}$

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

$\text{P(peach)}\times\text{P(orange)}=\frac{5}{14}\times\frac{2}{13}=\frac{5}{91}$

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 <===