The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university:

i. none will graduate,

ii. The only one will graduate,

iii. All will graduate.

Given that, the probability that a student entering a university will graduate is 0.4.

Let p be the probability that a student entering a university will graduate.

⇒ p = 0.4

Then, q is the probability of a student not graduating.

But, p + q = 1

⇒ q = 1 – p

Let X be a random variable that represents the number of students out of n students graduating after entering a university.

Then, the probability of r students out of n students graduating after entering a university is given by,

P (X = r) = ^{n}C_{r}p^{r}q^{n-r}

Here, a sample size of students, n = 3

Putting the value of n, p, and q in the above formula, we get

…(A)

(i). We need to find the probability that out of 3 students entering a university, none will graduate.

Put r = 0 in equation (A). We get

∴, the probability that none will graduate is 0.216.

(ii). We need to find the probability that out of 3 students only 1 will graduate.

So, put r = 1 in equation (A). We get

⇒ P (X = 1) = 0.432

∴, the probability that exactly one will graduate is 0.432.

(iii) We need to find the probability that out of 3 students all will graduate.

So, put r = 3 in equation (A). We get

⇒ P (X = 3) = 0.064

∴, the probability that all will graduate is 0.064.

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