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

Answer:

$\frac{20}{33}$

Step-by-step 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)=$\frac{number\;of\;favorable\;cases}{total\;number\;of cases}$

Using the formula of probability

$P(A)=\frac{8}{33}$

$P(B)=\frac{12}{33}$

$A\cap B=0$

$P(A\cap B)=0$

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

$P(A\cup B)=\frac{8}{33}+\frac{12}{33}$

$P(A\cup B)=\frac{8+12}{33}=\frac{20}{33}$

Hence, the probability of selecting a junior or senior=$\frac{20}{33}$