Question

Let S be a sample space and E and F be events associated with S. Suppose that Pr(E)=1/3, Pr(F)=3/10, and Pr(EUF)=2/5.

A. Pr(E ∩ F) = 1/15
B. Pr(E ∪ F') = 2/5
C. Pr(E' ∩ F') = 7/15
D. Pr(E' ∪ F) = 7/10

Answer 1

A. Pr(E ∩ F) = 1/15
B. Pr(E ∪ F') = 2/5
C. Pr(E' ∩ F') = 7/15
D. Pr(E' ∪ F) = 7/10

Step-by-step explanation:

A. Pr(E ∩ F) = 1/15

To find Pr(E ∩ F), we can use the formula:

Pr(E ∩ F) = Pr(E) + Pr(F) - Pr(E ∪ F)

Given that Pr(E) = 1/3, Pr(F) = 3/10, and Pr(E ∪ F) = 2/5, we can substitute these values into the formula:

Pr(E ∩ F) = 1/3 + 3/10 - 2/5

Simplifying the expression, we get:

Pr(E ∩ F) = 1/15

B. Pr(E ∪ F') = 2/5

To find Pr(E ∪ F'), we can use the formula:

Pr(E ∪ F') = Pr(E) + Pr(F') - Pr(E ∩ F')

Since E and F are mutually exclusive events (they cannot occur together), Pr(E ∩ F') is 0. Therefore, Pr(E ∪ F') simplifies to Pr(E) which is 1/3.

C. Pr(E' ∩ F') = 7/15

To find Pr(E' ∩ F'), we can use the formula:

Pr(E' ∩ F') = 1 - Pr(E ∪ F)

Given that Pr(E ∪ F) = 2/5, we can substitute this value into the formula:

Pr(E' ∩ F') = 1 - 2/5

Simplifying the expression, we get:

Pr(E' ∩ F') = 7/15

D. Pr(E' ∪ F) = 7/10

To find Pr(E' ∪ F), we can use the formula:

Pr(E' ∪ F) = 1 - Pr(E ∩ F')

Since E and F are mutually exclusive events (they cannot occur together), Pr(E ∩ F') is 0. Therefore, Pr(E' ∪ F) simplifies to 1 - Pr(E), which is 7/10.