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Question

There are 2 red and 2 yellow flowers in a basket. A child picks up at random three flowers. What is the probability of picking up both the yellow flowers?

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Solution

It is given that there are 2 red and 2 yellow flowers in a basket which means the total number of flowers are 4.

The number of ways of picking three flowers is:

4C3=4!(43)!×3!=4!1!×3!=4×3×2×11×3×2×1=4

Therefore, n(S)=4

Let A denote the event of picking three flowers out of which two are yellow, therefore,



n(A)=2C2×2C1=2!(22)!×2!×2!(21)!×1!=2!0!×2!×2!1!×1!=2×11×2×1×2×11×1=2



Thus, probability of picking three flowers out of which two are yellow is:



P(A)=n(A)n(S)=24=12



Hence, probability of picking up both the yellow flowers is 12.


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