Question

Find the missing probability.

P(A)=720,P(A∩B)=49400,P(B)=?
P
(
A
)
=
7
20
,
P
(
A
∩
B
)
=
49
400
,
P
(
B
)
=
?

Answer 1

Answer: P(B) = 7/20

==========================================

Work Shown:

Given info

P(A) = 7/20

P(A∩B)=49/400

P(B) = unknown

--------------------

P(A∩B) = P(A)*P(B), assuming A and B are independent events

49/400 = (7/20)*P(B)

(7/20)*P(B) = 49/400

P(B) = (20/7)(49/400)

P(B) = (20*49)/(7*400)

P(B) = (20*7*7)/(7*20*20)

P(B) = 7/20

---------------------

Note how

P(A∩B) = P(A)*P(B)

P(A∩B) = (7/20)*(7/20)

P(A∩B) = (7*7)/(20*20)

P(A∩B) = 49/400

which helps to confirm the answer.