Question

Given that P(A)=0.98, P(B)=0.37, and A and B are

independent:

Find P(A|B) (round to 2 decimals)

Find P(A or B) (round to 2 decimals)

Answer 1

Given that P(A) = 0.98, P(B) = 0.37, and A and B are independent, P(A|B) remains 0.98, and P(A or B) is calculated to be 0.99 after rounding to two decimals. P(A or B) = 0.9874, rounded to two decimals is 0.99.

Step-by-step explanation:

The problem requires us to find P(A|B) and P(A or B) given that the events A and B are independent and we are provided with their respective probabilities P(A)=0.98 and P(B)=0.37.

Since A and B are independent, the probability of A given B is the same as the probability of A alone. Therefore:

P(A|B) = P(A) = 0.98

When we want to find the probability of A or B occurring, we sum their individual probabilities and subtract the probability that they both occur:

P(A or B) = P(A) + P(B) - P(A)P(B)

So:

P(A or B) = 0.98 + 0.37 - (0.98 * 0.37)

P(A or B) = 1.35 - 0.3626

P(A or B) = 0.9874, rounded to two decimals is 0.99.