Question

Suppose that A and B are mutually exclusive events. Complete parts (a) and (b) below a. Use the special addition rule to express PiA or B) in terms of PIA) and P(B) Complete the equation below P(A or B) b. Show that the general addition rule gives the same answer as that in part (a) Select the correct answer below. O A. Since A and B are mutually exclusive events, then the probability that both A and Boccur is a That is PIA & B)- 0 Under these conditions, the general addtion rule gves the same answer O B. Since A and B are mutually exclusive events, then the probability that A or B occur is 1. That is, PA ) - PB ) - 1. Under these conditions, the general additon rule gives the same answer as that in part (a) Q c. Since A and B are mutually exclusive events, then the probability that both A and B occur is 0. That is, P(A)P(B)-0. Under these conditions, the general addition rule gives the same answer as that in part (a) O D. Since A and B are mutually exclusive events, then the probability that A or B occur is 1 That is, PA & B)- 1. Under these conditions, the general addition rule gives the same answer as that in part (a). that in part (a)

Answer 1

Answer:

a)

Here we can say that A and B are the mutually exclusive events which is according to the special addition rule

i.e.,

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

So that P(A or B) is expressed in terms of P(A) and P(B)

b)

Here the general addition gives the answer i.e., as follows

we know that according to general addition rule

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

since the events A and B are mutually exclusive so P(A & B) = 0

so

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

P(A or B) = P(A) + P(B) - 0

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

By observing we can say that

option A is correct answer

i.e.,

Since A and B are the mutually exclusive events then the probability that both A and B occur is 0 i.e., P(A&B) = 0 under these conditions the general addition rule gives the same answer as that in part(a)