Question

the table shows the foreign language that students are taking. match the probability with the description.

	spanish	french	german	total
girls	15	12	3	30
total	25	14	11	50

find p(boys)
find p(french)
find p(german and girls)
find p(boys | spanish)
find p(french | girls)
find p(girls | german)

Explanation:

Step1: Recall probability formula

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Find P(boys)

The number of boys is 20 and the total number of students is 50. So $P(\text{boys})=\frac{20}{50}$.

Step3: Find P(French)

The number of students taking French is 14 and the total number of students is 50. So $P(\text{French})=\frac{14}{50}$.

Step4: Find P(German and Girls)

The number of girls taking German is 3 and the total number of students is 50. So $P(\text{German and Girls})=\frac{3}{50}$.

Step5: Find P(Boys | Spanish)

The formula for conditional - probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $A$ is the event of being a boy and $B$ is the event of taking Spanish. The number of boys taking Spanish is 10 and the number of students taking Spanish is 25. So $P(\text{Boys}|\text{Spanish})=\frac{10}{25}$.

Step6: Find P(French | Girls)

The number of girls taking French is 12 and the number of girls is 30. So $P(\text{French}|\text{Girls})=\frac{12}{30}$.

Step7: Find P(Girls | German)

The number of girls taking German is 3 and the number of students taking German is 11. So $P(\text{Girls}|\text{German})=\frac{3}{11}$.

Answer:

P(boys): 20/50
P(French): 14/50
P(German and Girls): 3/50
P(Boys | Spanish): 10/25
P(French | Girls): 12/30
P(Girls | German): 3/11