Question

The probability that a student studying in 12th standard of science stream will get admission to engineering branch is 0.3. 5 students are selected from the students who studied in this stream. Find the probability of the event that the number of students admitted to engineering branch is more than the number of students who did not get admission to the engineering branch.

Answer 1

Here, n = 5

p = Probability that a student will get admission to engineering branch = 0.3

∴ q = 1 – p = 1 – 0.3 = 0.7

X is binomial random variable.

∴ P(X = X) = p(x) = ⁿC_xp^xq^n-x

Putting, n = 5, p = 0.3, q = 0.7

P(X = x) = p(x) = ⁵C_x(0.3)^x(0.7)^5-x

X = At least three students will get admission in engineering branch

∴ X ≥ 3

Now, P(X ≥ 3) = p(3) + p(4) + p(5)

= [⁵C₃(0.3)³ (0.7)^{5 – 3}] + [⁵C₄(0.3)⁴(0.7)^{5 – 4}] + [⁵C₅(0.3)⁵ (0.7)^{5 – 5}]

= [10(0.027) (0.7)²] + [5(0.0081) (0.7)¹] + [1 (0.00243) (0.7)⁰]

= [10 × 0.027 × 0.49] + [5(0.0081) (0.7)] + [1 × 0.00243 × 1]

= 0.1323 + 0.02835 + 0.00243

= 0.16308
= 0.1631