Question

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

Answer 1

The right answer for the question that is being asked and shown above is that: "E. The probability that Jacqueline and Marc both can solve a problem in a math test is 0.52; B. The probability that Jacqueline and Marc both can solve a problem in a math test is 0.93."

Answer 2

Option A , D and E holds.

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 :

=
`P(J) * P(M)`

=
`0.80*0.65`

=
`0.52`

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 :
`P(A) * P(B)=P(A \cap B)`

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

Hence Option A , D and E holds.