Question

Use the formula for conditional probability to find the probability: for events Q and R.

P(Q) = 0.88, P(R) = 0.76. P(R and Q) = 0.49. Find the value of the probability P(RQ).

Answer 1

The conditional probability P(R|Q) is found using the formula P(A|B) = P(A AND B) / P(B), which for our values is 0.49 / 0.88, giving us P(R|Q) = 0.557.

Step-by-step explanation:

To find the conditional probability P(R|Q), we use the formula for conditional probability:

P(A|B) = ​P(A AND B) / P(B)

Given that P(Q) = 0.88, P(R) = 0.76, and P(R AND Q) = 0.49, we can plug in the values to find P(R|Q):

​P(R|Q) = ​P(R AND Q) / P(Q) = 0.49 / 0.88

Now, performing the division, we get:

​P(R|Q) = 0.5568, which can be rounded to 0.557 when expressed to three decimal places.