Question

In a high school class, 50% of the students took Spanish, 25% took French and 30% of the

students took neither. Let A be the event that a randomly chosen student took Spanish,
and B be the event that a student took French. Fill in either the Venn diagram or a 2-way
table and answer the questions:
a) Describe in words the meaning of the event
AB'
. Find the probability of this event.
b) Are the events A, B independent? Explain with numbers why or why not.
c) If it is known that the student took Spanish, what are the chances that she also took
French?

Answer 1

Answer:Here is a Venn diagram for the events:

Explanation:

French

________

| |

| B |

|________|

\ /

\ /

\ /

Spanish \/

A

a) The event AB' represents the students who took Spanish but not French. The probability of this event is the combined area of the shaded region in the Venn diagram. This can be calculated as P(A) - P(AB) = 0.5 - 0.25 = 0.25.

b) No, the events A and B are not independent. Independence means that the probability of one event occurring is not affected by the occurrence of another event. But in this case, if a student takes Spanish, the probability that they also took French is not the same as the probability that any randomly chosen student took French, i.e. P(B|A) ≠ P(B).

c) If it is known that the student took Spanish, then the chances that she also took French is given by P(B|A) = P(AB) / P(A) = 0.25 / 0.5 = 0.5. This means that 50% of the students who took Spanish also took French.