Question

P(A) = 1/3 and P(B) = 2/3. Find the value of P(A AND B).
Select one:
O a. 1/6
O b. 2/9
O c.215
O d. 1/5
​

Answer 1

Step-by-step explanation:

Given P(A)=1/2 and P(B)=1/5

we know that for two independent events A,B.

⇒ P(A∩B)=P(A)*P(B)

⇒P(A∩B)=1/2∗1/5=1/10

⇒1) P(A∪B)=P(A)+P(B)-P(A∩B)

=1/2+1/5−1/10

=3/5

⇒2) P(A/B)=P(A∩B)/P(B)

=

(1/5)

(1/10)

=

2

1

3)P(A/A∪B)=P(A∩(A∪B))/P(A∪B) [ since P(A∩(A∪B))=P(A)]

P(A/A∪B)=P(A)/P(A∪B)

=

(3/5)

(1/2)

=

6

5

4)P(A∩B/(A

′

∪B

′

)=

P(A

′

∪B

′

)

P((A∩B)∩(A

′

∪B

′

))

=

P(A

′

∪B

′

)

P((A∩B)∩(A∩B)

′

)

=0

Answer 2

Answer:

c. is the correct answer