Two psychologists surveyed 478 children in grades 4, 5 and 6 in elementary schoo

Question

Two psychologists surveyed 478 children in grades 4, 5 and 6 in elementary schools in Michigan. They asked the students whether their primary goal was to get good grades, to be popular, or to be good at sports. Here's a contingency table giving counts of the students by their goals and sex: a. What is the probability of selecting a girl whose goal is to be popular? b. What is the probability of selecting a student whose goal is to excel at sports? c. What is the probability of selecting a boy whose goal is to get good grades?

Explanation / Answer

From the data given, we can rewrite it as

(a) What is the probability of selecting a girl who is popular.

Here there is a combination of 2 probabilities:

P(A)= probability of selecting a girl = 251/478 and P(B) = probability of selecting a girl who wants to be popular = 91/251

Therefore the required probability is P(A) * P (B) = (251/478)* (91/251) = 91/478 = 0.190

(b) What is the probability of selecting a student whose goal is to excel ata sports

There are 90 students out of 478 who want to excel in sports.

Therefore the required probability = 90/478 = 0.188

(c) What is the probability of selecting a boy whose goal is to get good grades.

Here again there is a combination of 2 probabilities:

P(A)= probability of selecting a boy = 227/478 and P(B) = probability of selecting a boy who wants good grades = 117/227

Therefore the required probability is P(A) * P (B) = (227/478)* (117/227) = 117/478 = 0.245

Sex/Goal Grade Popular Sports Total Boy 117 50 60 227 Girl 130 91 30 251 Total 247 141 90 478

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