SOLUTION: a group of students contains 60% females and 40% males. Suppose 30% of the females have long hair and 20% of the males have long hair. what is the probability that a student chosen

Question 1119031: a group of students contains 60% females and 40% males. Suppose 30% of the females have long hair and 20% of the males have long hair. what is the probability that a student chosen at random from the group have a short hair
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
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Let X be the total number of students in the group. Then the number of females is 0.6X, while the number of males is 0.4X. The number of females with short hair is 0.7*(0.6X) = 0.42X, (<<<---=== 0.7 = 1-0.3 ) while the number of males with short hair is 0.8*(0.4X) = 0.32X. (<<<---=== 0.8 = 1-0.2 ) Thus the total number of individuals with short hair is 0.42X + 0.32X = 0.74X. Then the probability under the question is = 0.74 = 74%.

Solved.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Many students find it easier to solve problems like this by putting numbers to the problem instead of working with the percentages. Since the students are 60% female and 40% male, using 60 females and 40 males makes good sense.

Then 30% of the females (30% of 60 = 18) and 20% of the males (20% 0f 40 = 8) have long hair. That leaves 60-18 = 42 females and 40-8 = 32 males with short hair, for a total of 42+32 = 74.

Then since 74 out of the 100 students have short hair, the probability that a randomly chosen student will have short hair is 74/100, or 74%.
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