Question

Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 6 18 3 27 Female 13 20 12 45 Total 19 38 15 72 If one student is chosen at random,
If one student is chosen at random,
Find the probability that the student got a B:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got an "B":
If one student is chosen at random, find the probability that the student got a 'B' GIVEN they are male:

Answer 1

Answer:

P(Got a B) = $\frac{19}{36}$

P(Female AND got a C) = $\frac{1}{6}$

P(Female or Got an B =  $\frac{7}{8}$

P(got a 'B' GIVEN they are male) =  $\frac{9}{19}$

Step-by-step explanation:

Given:

       A B C Total

Male 6 18 3 27

Female 13 20 12 45

Total 19 38 15 72

We know that the probability = The number of favorable outcomes ÷ The total number of possible outcomes.

Total number = 72

1) If one student is chosen at random, Find the probability that the student got a B:

Got B = 38

P(Got a B) = $\frac{38}{72}$

Simplifying the above probability, we get

P(Got a B) = $\frac{19}{36}$

2) Find the probability that the student was female AND got a "C":

Female AND got a C = 12

P(Female AND got a C ) = $\frac{12}{72}$

Simplifying the above probability, we get

P(Female AND got a C) = $\frac{1}{6}$

3) Find the probability that the student was female OR got an "B":

Female OR got an B = Total number of female + students got B - Female got 20

= 45 + 38 - 20

= 73 - 20

= 63

P(Female OR got an B ) =  $\frac{63}{72}$

P(Female or Got an B =  $\frac{7}{8}$

4) If one student is chosen at random, find the probability that the student got a 'B' GIVEN they are male:

Total number of students who got B  = 38

Student got a B given they are male = 18

P(got a 'B' GIVEN they are male) =  $\frac{18}{38}$

P(got a 'B' GIVEN they are male) =  $\frac{9}{19}$