Question

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In a certain group of students, the probability of a randomly-chosen student male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a maile who studies Spanish is 5%. What is the probability of the student studying Spanish, if you know the student is male?

a. 7.2%
b. 12.5%
c. 8%
d. About 27.8%

Answer 1

b. 12.5%

Explanation:

To determine the probability of the student studying Spanish given that the student is male, we can use conditional probability.

In this case:

• Let M be the event that a student is male.
• Let S be the event that a student studies Spanish.

The given probabilities are:

• P(M) = 0.4 (probability of a student being male)
• P(S) = 0.18 (probability of a student studying Spanish)
• P(M ∩ S) = 0.05 (probability of a male student studying Spanish)

The probability of a student studying Spanish given that the student is male, denoted as P(S | M), can be calculated using the formula for conditional probability:

`\boxed{\begin{array}{c}\underline{\sf Conditional\;Probability\;}\\\\\sf P(S|M)=(P(M \cap S))/(P(M))\end{array}}`

Substitute the given probabilities:

`\sf P(S|M)=(0.05)/(0.40)=0.125=12.5\%`

Therefore, the probability of a student studying Spanish, given that the student is male, is 12.5%.