Probability, 5 bananas 5 apples?

Question

A basket contains 5 bananas and 5 apples. Each of five persons picks two fruits at random from the basket without replacement.
(A) what is the probability that the first person picks one apple and one banana.
(B) what is the probability that everyone picks exactly one apple and one banana?

Answer 1

Step 1:

(a)

A basket have 5 bananas and 5 apples.

A group of 5 persons, each person picking 2 fruits with out replacement.

Number of way each person picking 2 fruits from basket is

The probability that the first person picks one -

-apple and one banana =

Solution :

The probability that the first person picks one apple and one banana is 0.556.

Answer 2

Step 1:

(b)

The probability that everyone picks exactly one apple and one banana :

The probability that the first person picks one apple and one banana is .

The remaining apples are 4 and remaining bananas are 4.

So the probability of second person picks one apple and one banana is .

The remaining apples are 3 and remaining bananas are 3.

The probability of third person picks one apple and one banana is .

The remaining apples are 2 and remaining bananas are 2.

The probability of fourth person picks one apple and one banana is .

The remaining apples are 1 and remaining bananas are 1.

The probability of last person picks one apple and one banana is 1.  (Since the the remaining apples are 1 and remaining bananas are 1 ).

Step 2:

The probability that everyone picks exactly one apple and one banana is :

Solution :

The probability that everyone picks exactly one apple and one banana is 0.158.