Question

The probability of event A is 0.48, the probability of event A and B is 0.21, and the probability of events A or B is 0.89. What is the probability of event B?

Answer 1

0.62

Explanation:

Answer 2

`P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89`

And for this case we can use the total rule of probability given by:

`P(A \cup B) = P(A) +P(B) -P(A\cap B)`

And if we solve for
`P(B)` we got:

`P(B)= P(A \cup B) -P(A) +P(A \cap B)`

And replacing we got:

`P(B) = 0.89 -0.48 +0.21= 0.62`

Explanation:

We have the following probabilities given:

`P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89`

And for this case we can use the total rule of probability given by:

`P(A \cup B) = P(A) +P(B) -P(A\cap B)`

And if we solve for
`P(B)` we got:

`P(B)= P(A \cup B) -P(A) +P(A \cap B)`

And replacing we got:

`P(B) = 0.89 -0.48 +0.21= 0.62`