Question 1210443
<pre>
Giving a test to a group of students, the grades and gender are summarized
below:
        A   B   C Total
Male   16  22  32    70
Female 13  17  25    55
Total  29  39  57   125
Determine the following probabilities. Write your answers as reduced fractions.
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We randomly select a student. What is the probability that this student got a B?
P(B) = 39/125
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We randomly select a student. What is the probability that this student is a male who got a B?
P(M AND B) = 22/125
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We randomly select a male student. What is the probability that he got a B?
P(B|M) = P(B AND M)/P(M) = {{{(22/125)/(70/125) = 22/70 = 11/35}}}
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We randomly select a student who got a B. What is the probability that this student is a male?
P(B|M) = P(M AND B)/P(B) = {{{(22/125)/(39/125) = 39/70}}}

Edwin</pre>