Question

Of 10 people in an office, 6 are women and 4 are older than 30. Of the people over 30, 2 are women. Which is the probability that one of the people is a woman or over 30?

Answer 1

Given:

Total number of people in the office = 10

Number of women = 6

Number of people older than 30 = 4

Number of people older than 30 who are women = 2

Let's find the probability that one of the people is a woman or over 30.

• To find the probability, apply the formula:

$P(\text{Woman }\cup\text{ over 30)= }P(\text{woman) + P(over 30) - P(woman }\cap\text{ over 30)}$

Thus, we have:

$P(\text{woman or over 30) = }\frac{6}{30}+\frac{4}{30}-\frac{2}{30}=\frac{6+4-2}{30}=\frac{8}{30}=\frac{4}{15}$

Therefore, the probability that one of the people is a woman or over 30 is:

$\frac{4}{15}$

ANSWER:

$\frac{4}{15}$