Question

Of 570 people, 375 were male and 357 had brown hair. Of those with brown hair, 108 were female. What is the probability that a person was male or had brown hair. Give your answer in decimal form, rounded to the nearest hundredth.

Answer 1

The probability that a person was male or had brown hair is 0.99 when rounded to the nearest hundredth.

Step-by-step explanation:

To find the probability that a person was male or had brown hair, we use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B). First, let's identify our values:

• Total people: 570
• Number of males: 375
• Number of people with brown hair: 357
• Number of females with brown hair: 108

Since there are 108 females with brown hair, the number of males with brown hair is 357 - 108 = 249. Note that 108 females with brown hair are already included in the total number of people with brown hair (357).

To find the number of males or people with brown hair, we need to avoid double counting the males with brown hair. The math is as follows:

P(Male or Brown Hair) = P(Male) + P(Brown Hair) - P(Male and Brown Hair)

P(Male) = 375/570

P(Brown Hair) = 357/570

P(Male and Brown Hair) = 249/570

So,

P(Male or Brown Hair) = (375/570) + (357/570) - (249/570) = 0.9868

Rounded to the nearest hundredth, the probability is 0.99.