Given a sample space, and events a and b, where p(a)= 0.5 and p(b)=0.5. which of the following values for p(a and b) are not possible?
a. all are possible
b. 0.35
c. 0.5
d. 0
e. 0.25

Option a, option b, option c, option d are not possible values for P(A ∩ B)

Solution:

Given A and B are independent events.

P(A) = 0.5 and P(B) = 0.5

To find which of the following values for P(A and B) are not possible.

P(A and B) = P(A ∩ B)

P(A ∩ B) = P(A) × P(B)

              = 0.5 × 0.5

P(A ∩ B) = 0.25

Option a: All are possible.

All answers are not possible for two independent events.

Option b: 0.35

We found that P(A and B) is 0.25.

So, 0.35 is not possible value.

Option c: 0.5

We found that P(A and B) is 0.25.

So, 0.5 is not possible value.

Option d: 0

We found that P(A and B) is 0.25.

So, 0 is not possible value.

Option e: 0.25

We found that P(A and B) is 0.25.

So, 0.25 is the possible value.

Hence, 0.35, 0.5, 0 are not possible values.

yes

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step-by-step explanation:

answer:   (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)