Question

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.

Options

• 0.9851

• 0.9185

• 0.9245

• 0.9254

Answer 1

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is 0.9185.

Explanation:

Here, n = 5

r = 0, 1

p = `10/100 = 1/10`

q = `1 - 1/10 = 9/10`

Required probability,

P(X ≤ 1) = P(X = 0) + P(X = 1)

`= ""^5C_0 (9/10)^5 + "^5C_1 (1/10)^1 (9/10)^4`

`= (9/10)^5 + (5 xx 9^4)/10^5`

`= 9^4/10^5 (9 + 5) = (9^4 xx 14)/10^5`

`= 91854/100000`

= 0.91854

= 0.9185