Question

In a statistics class of 13 sophomores, 12 juniors, and 8 seniors, 5 of whom are male sophomores, 6 of whom are female juniors, and 4 of whom are male seniors, what is the probability of randomly selecting a junior or a senior?

Answer 1

`(20)/(33)`

Explanation:

We are given that

Sophomores=13

Juniors=12

Seniors=8

Male sophomores=5

Female sophomores=6

Male seniors=4

We have to find the probability of randomly selecting a junior or a senior.

Total persons=13+12+8=33

Let A=Seniors

B=Juniors

Probability,P(E)=
`(number\;of\;favorable\;cases)/(total\;number\;of cases)`

Using the formula of probability

`P(A)=(8)/(33)`

`P(B)=(12)/(33)`

`A\cap B=0`

`P(A\cap B)=0`

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

`P(A\cup B)=(8)/(33)+(12)/(33)`

`P(A\cup B)=(8+12)/(33)=(20)/(33)`

Hence, the probability of selecting a junior or senior=
`(20)/(33)`