Question

Jacqueline and Marc both took a math test. Jacqueline solved 80% of the problems correctly whereas Marc solved only 65% of the problems correctly.

If we select a problem at random from this test,

let the event J be that Jacqueline solved the problem correctly,
and the event M be that Marc solved the problem correctly.
Select all that apply.

P(J) × P(M) = P(J ∩ M)
The probability that Jacqueline and Marc both solved the problem correctly is 0.93.
The probability that Jacqueline and Marc both solved the problem correctly is 0.52.
P(J) × P(M) = P(J ∪ M)
J and M are independent events.

Answer 1

We have:

P(J) = 80% = 0.8
P(M) = 65% = 0.65

We can state that:

- P(J) × P(M) = P(J ∩ M), correct

- The probability that Jacqueline and Marc both solved the problem correctly is 0.93., incorrect as 0.8*0.65 is not same as 0.93

- The probability that Jacqueline and Marc both solved the problem correctly is 0.52, correct as 0.8*0.65 = 0.52

- P(J) × P(M) = P(J ∪ M), incorrect as conflicts with option 1.

- J and M are independent events, correct as option 1 is true and is confirmed by option 3.