Question

A test tube contains 25 bacteria, 5 of which are can stay alive for atleast 30 days, 10 of which will die in their second day. 10 of which are already dead.
Given that a randomly chosen bacteria for experiment is alive. What is the probability it will still be alive after one week?
(a)1 ⁄ 3(b)2 ⁄3
(c) 1⁄5 (d)4 ⁄5

Answer 1

Answer:

c. $\frac{1}{5}$

Step-by-step explanation:

Given,

Number of bacterias who alive for at least 30 days = 5,

Bacterias who alive for 2 days = 10,

Died bacterias = 10,

Total bacterias = 5 + 10 + 10 = 25,

Ways of choosing a bacteria = $^{25}C_1$ = $\frac{25!}{1! 24!}$ = 25,

While, ways of choosing of a bacteria who will live after 1 week = $^5C_1$ = $\frac{5!}{1!4!}$ = 5,

Hence, the probability it will still be alive after one week = $\frac{5}{25}$ = $\frac{1}{5}$

OPTION C is correct.