Question

Five men in a company of 20 are graduates. if 3 men are picked out of the 20 at random. what is the probability that they are all graduates? what is the probability of at least one graduate?

Answer 1

the ans is 1/4 for graduate

Answer 2

Answer: Probability of getting all graduates is $\dfrac{1}{114}$ and Probability of getting at least one graduate is $\dfrac{137}{228}$

Step-by-step explanation:

Since we have given that

Total number of people in a company = 20

Number of people are graduates = 5

3 men are picked out of 20 randomly.

We need to find the probability that they are all graduates.

So, Probability becomes,

$\dfrac{^5C_3}{^{20}C_3}\\\\=\dfrac{10}{1140}\\\\=\dfrac{1}{114}$

And probability of at least one graduate is given by

P(atleast one graduate)=1-P(No graduate)

$1-\dfrac{^{15}C_3}{^{20}C_3}\\\\\\=1-\dfrac{455}{1140}\\\\\\=\dfrac{1140-455}{1140}\\\\\\=\dfrac{685}{1140}\\\\\\=\dfrac{137}{228}$

Hence, Probability of getting all graduates is $\dfrac{1}{114}$ and Probability of getting at least one graduate is $\dfrac{137}{228}$