Question

ABС154Giving a test to a group of students, the grades and gender are summarized below. Round youranswers to 4 decimal places.Grades and GenderTotalMale1433Female 3 1021Total 18 24 1254If one student is chosen at random,a. Find the probability that the student got a B:8b. Find the probability that the student was female AND got an "A":C. Find the probability that the student was male OR got a "B":d. If one student is chosen at random, find the probability that the student got an 'B' GIVEN they arefemale:Calculator

Answer 1

a. Probability that the student got a B = 24/54 = 0.444444

= 0.4444 (4 decimal places)

b. Probability that the student was female AND got an "A":

$\begin{gathered} \text{ = }\frac{3}{54} \\ =0.055555 \\ =0.0556\text{ (4 decimal places)} \end{gathered}$

c.

Probability that the student was male OR got a "B"

$\begin{gathered} \text{ }\frac{33}{54}\text{ + }\frac{24}{54}-\frac{14}{54}\text{ = }\frac{43}{54}\text{ } \\ =0.796296 \\ =0.7963\text{ (4 decimal places)} \end{gathered}$

d. Probability that the student got an 'B' GIVEN they are female

$\begin{gathered} \text{ }\frac{p(B\text{ n Female)}}{p(\text{Female)}} \\ =\frac{10}{21} \\ =0.47619048 \\ =0.4762\text{ (4 decimal places)} \end{gathered}$