Question

A basket contains 15 apples and 10 oranges out of which 4 apples and 2 oranges are defective. If a person takes two fruits at random, what is the probability that either both are apples or both are good221/300

Answer 1

Total outcomes=15 apples +10 oranges=25

P(both are apples and both are good)=11/25

P(both are apples) =15/25

P(defective apple) =4/25

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Answer 2

The probability is 221/300

Given:

Total number of apples = 15

Total number of oranges = 10

Defective apples = 4

Defective oranges = 2

To Find:

Probability that either both are apples or both are good

Solution:

Total number of fruits = 10 + 15 = 25

Total good fruits = 25 - ( 4 + 2)

= 25 - 6 = 19

Number of ways in which two fruits can be taken from  25 fruits = 25C2

Number of ways in which two apples can be taken from 15 apples = 15C2

Therefore,

P(both are apples) = 15C2/25C2

Number of ways in which two fruits taken can be taken from  19 good fruits = 19C2

P(both are good) = 19C2/25C2

Number of ways in which two apples can be taken from 11 good apples = 11C2

P(both are apples and both are good) = 11C2/19C2

Solving -

15C2/25C2 + 19C2/25C2 - 11C2/19C2

= 221/300

Answer: The probability is 221/300

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