Select all that apply.

jacqueline solved 80% of problems correctly in a math test whereas marc solved only 65% of the problems correctly.

let the event j = correct problems solved by jacqueline,
and the event m = correct problems solved by marc.
a. p(j) × p(m) = p(j ∩ m)
b. the probability that jacqueline and marc both can solve a problem in a math test is 0.93.
c. p(j) × p(m) = p(j ∪ m)
d. j and m are independent events.
e. the probability that jacqueline and marc both can solve a problem in a math test is 0.52

Option A , D and E holds.

Step-by-step explanation:

Let the event J = correct problems solved by Jacqueline,

and the event M = correct problems solved by Marc.

Jacqueline solved 80% of problems correctly in a math

So, probability of correct problems solved by Jacqueline P(J)=0.80

Marc solved only 65% of the problems correctly.

So, probability of correct problems solved by Marc P(M)=0.65

Probability of correct problems Solved by Marc and Jacqueline :

=

=  

=  

So, Option E is correct.

we also know that and means intersection .

So, P(J) × P(M) = P(J ∩ M)

So, Option A is also correct.

Since option A holds .

So, property of independent events is satisfied :

Thus Option D also holds.J and M are independent events.

Hence Option A , D and E holds.