Question

If three mangoes are taken one after the other from a basket which contain 10 ripe and 4 unripe

mangoes

1. What is the probability that you will get 3 ripe mangoes?

2. What is the probability that you will get 2 ripe mangoes?

3. What is the probability that you will get 1 ripe mango?

4. What is the probability that you will not get ripe mango?

Answer 1

We can take three mangoes in $\dbinom{10+4}{3}=364$ possible ways.

1.

$$P(3\ ripe)=\dfrac{\dbinom{10}{3}\dbinom{4}{3-3}}{\dbinom{14}{3}}=\dfrac{120(1)}{364}=\dfrac{30}{91}$$

2.

$$P(2\ ripe\ \& \ 1\ unripe)=\dfrac{\dbinom{10}{2}\dbinom{4}{3-2}}{\dbinom{14}{3}}=\dfrac{45(4)}{364}=\dfrac{45}{91}$$

3.

$$P(1\ ripe\ \& \ 2\ unripe)=\dfrac{\dbinom{10}{1}\dbinom{4}{3-1}}{\dbinom{14}{3}}=\dfrac{10(6)}{364}=\dfrac{15}{91}$$

4.

$$P(3\ unripe)=\dfrac{\dbinom{10}{0}\dbinom{4}{3-0}}{\dbinom{14}{3}}=\dfrac{1(4)}{364}=\dfrac{1}{91}$$