Question

One hundred people were asked if they prefer Math, Science or Social Studies. The results are thefollowing:56 prefer Math43 prefer Science35 prefer Social Studies6 prefer all three subjects18 prefer Math and Science10 prefer Science and Social Studies12 prefer Math and Social StudiesMy questions 1. How many people prefer only Math? 32 People 2. How many people prefer only Science?21 People ^ I just need clarification those are right Help with these>> 3. If one person is chosen at random, what is the probability they will prefer Science and Math?4. If one person is chosen at random, what is the probability they will prefer only Math?5. If one person is chosen at random, what is the probability they will not prefer Science?6. Given that the person prefers Social Studies, what is the probability they prefer Math?

Answer 1

Statement Problem(6) : Given that the person prefers Social Studies, what is the probability they prefer Maths.

Solution:

The conditional probability of A given B is defined as;

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Let S be number of people that prefer Social Studies and let M be number of people that prefer Math.

Hence, the probability they prefer Math given that the person prefers Social Studies is;

$\begin{gathered} P(M|S)=\frac{P(M\cap S)}{P(S)} \\ P(M|S)=\frac{18}{100}\div\frac{35}{100} \\ P(M|S)=\frac{18}{35} \end{gathered}$