Question

The probability of a student possessing a Hi-Tech point pen is 3/5 and that of possessing a ball point pen is 2/3. Find the probability that a student can have at least one type of pen. ​

Answer 1

Probability that student can have AT LEAST one type of pen is 13/15

Step-by-step explanation:

1) We have,

A : Event that student possess Hi Tech point pen

B : That of Ball point pen.

We have,

P(A) = 3/5

P(B)=2/3

Then, Probability that student can have at least one type of pen is same as complement of having none of them.

2) Hence,

$P(at\:least\:one ) = 1-P(none\:of\:them) \\ \\ = 1-P(A^c)P(B^c) \\ \\ = 1-(1-3/5)(1-2/3)\\ \\ =1-\frac{2}{5}*\frac{1}{3}\\ \\=\frac{13}{15}$

Hence,

Required Probability is 13/15.