Question

Superpowers A random sample of $415$children from England and the United States who completed a survey in a recent year was selected. Each student’s country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the two-way table.

Suppose we randomly select one of these students. Define events E: England, T: telepathy,

and S: superstrength.

a. Find $P(T|E)$. Interpret this value in context.

b. Given that the student did not choose superstrength, what’s the probability that this child is from England is ? Write your answer as a probability statement using correct symbols for the events.

Short answer

a. The value of $P(T/E)=44/200$

b. The probability that this child is from England is $180/372$

Step-by-step solution

 Part (a) Step 1: Given information

We need to find the value of $P(T/E)$

 Part (a) Step 2: Explanation

Here , we will use the formula for conditional probability ;

$$\begin{gathered} P(T\cap E)=\frac{44}{415} \\ P\left(E\right)=\frac{200}{415} \\ P(T/E)=\frac{P(T\cap E)}{P\left(E\right)}=\frac{44}{200} \end{gathered}$$

 Part (b) Step 1: Given information

We need to find the probability that this child is from England.

 Part (b) Step 2: Explanation

Here , we will use conditional probability as condition is given ;

Let E is event that child is from england and S is event that student did not choose superstrength ;

So we need to find -$P(E/S)=\frac{P(E\cap S)}{P\left(S\right)}=\frac{180/415}{372/415}=\frac{180}{372}$