Question

A box contains 3 lemons and 6 apples. We draw two fruits at random. What's the probability of getting 2 lemons

Answer 1

Answer: The answer is $\dfrac{1}{12}.$

Step-by-step explanation:  Given that in a box, there are 3 lemons and 6 apples And we draw two fruits at random. We are to find the probability of getting 2 lemons.

Total number of fruits = 3 + 6 = 9.

Number of ways in we can choose 2 lemons out of 3 lemons is given by

$n_1=\dfrac{3!}{2!(3-2)!}=\dfrac{3\times 2!}{2!\times 1!}=3,$

and the number of ways in which we can choose 2 lemons out of 9 fruits is

$n_2=\dfrac{9!}{2!(9-2)!}=\dfrac{9\times 8\times 7!}{2\times 1\times 7!}=36.$

Therefore, required probability is

$p=\dfrac{n_1}{n_2}=\dfrac{3}{36}=\dfrac{1}{12}.$

Thus, the answer is $\dfrac{1}{12}.$