Question

Suppose a math class has 16 females (4 of whom speak French) and 15 males (5 of whom speak French).Compute the probability that a randomly selected student is male, given that the student speaks French.Round your answer to three decimal places.

Answer 1

Answer:

The probability that a randomly selected student is male, given that the student speaks French is 0.556

Explanation:

Given:

Number of females in the math class = 16

4 of the females speak french

Number of males in the math class = 15

5 of the males speak french

To find:

the probability that a randomly selected student is male, given that the student speaks French

To determine the probability, we will construct a table and fill in the numbers under each of the headings

The probability that a randomly selected student is male, given that the student speaks French:

$\begin{gathered} The\text{ probability is a conditional probability and it is calculated as:} \\ P(M|Fr)\text{ = }\frac{P(M\text{ and Fr\rparen}}{P(Fr)} \\ \\ where\text{ M}=\text{ males} \\ Fr\text{ = French} \end{gathered}$$\begin{gathered} P(M\text{ and Fr\rparen = intersection of Males and does who speak French } \\ P(M\text{ and Fr\rparen = 5} \\ \\ P(Fr)\text{ = Total of those whose speak French} \\ P(Fr)\text{ = 9} \end{gathered}$$P(M|Fr)\text{ = }\frac{5}{9}\text{ = 0.556}$