Answer to Question #119673 in Statistics and Probability for Sydney Casillas

Question

Giving a test to a group of students, the grades and gender are summarized below

A B C Total
Male 17 8 5 30
Female 18 19 3 40
Total 35 27 8 70


If one student is chosen at random,

Find the probability that the student was female OR got an "B".

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} & A & B & C & Total \\ \hline Male & 17 & 8 & 5 & 30 \\ \hdashline Female & 18 & 19 & 3 & 40 \\ \hdashline Total & 35 & 27 & 8 & 70 \end{array}$$

$$P(F\cup B)=P(F)+P(B)-P(F\cap B)=$$

$$={40\over 70}+{27\over 70}-{19\over 70}={24\over 35}$$

 The probability that the student was female OR got an "B"is $\dfrac{24}{35}.$