In a bag there are a total of 60 fruits. The average of the number of apples and mangoes in the bag is equal to the number of bananas in the bag. The ratio between the number of apples and bananas in the bag is 5:4 respectively. Find out the probability of picking two fruits from the bag such that at least one of them is an apple.

Solution

The ratio between the number of apples and bananas in the bag is 5:4 respectively.

Let’s assume the number of apples and bananas in the bag is 5y and 4y respectively.

The average of the number of apples and mangoes in the bag is equal to the number of bananas in the bag.

(5y+number of mangoes)/2 = 4y

5y+number of mangoes = 8y

number of mangoes = 8y-5y = 3y

In a bag there are a total of 60 fruits.

5y+3y+4y = 60

12y = 60

y = 5

Number of apples = 5y = 5x5 = 25

Number of mangoes = 3y = 3x5 = 15

Number of bananas = 4y = 4x5 = 20

Probability of picking two fruits from the bag such that at least one of them is an apple = (25C1 x 35C1 + 25C2)/(60C2)

= (25x35+300)/( 1770 )

= (875+300)/( 1770 )

= 1175/ 1770

= 235/354