Question

A basket contains 7 apples and 14 oranges. if we select two at random, then what is the probability that both are different?

Answer 1

Given:

The number of apples = 7.

The number of oranges = 14.

The total number of fruits = 21.

The number of fruits drawn at a time = 2.

To Find:

If two fruits are selected at random, we have to find out the probability that both are different.

Solution:

The total number of fruits is given as 21.

The probability of the first pick being an apple = $\frac{7}{21}$.

If the first pick is an apple, then the probability of the second pick being an apple = $\frac{6}{20}$.

∴, The probability of both picks being an apple = $\frac{7}{21}$ × $\frac{6}{20}$ $= \frac{42}{420}$.

Similarly, the probability of the first pick being an orange = $\frac{14}{21}$.

If the first pick is an orange, then the probability of the second pick being an orange = $\frac{13}{20}$.

∴, The probability of both picks being an orange =  $\frac{14}{21}$ × $\frac{13}{20}$ $= \frac{182}{420}$.

The probability that both the picks are same  $= \frac{42}{420} + \frac{182}{420} = \frac{224}{420}$.

The total probability of any event = 1.

∴, The probability that both the picks are different $= 1 - \frac{224}{420} = \frac{196}{420} = \frac{7}{15}$.

Hence, the probability that both are different if selected at random is $\frac{7}{15}$.

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