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Question

Find each of the following probabilities if the probability that Aramark stock (event A) rises is 46.4%, and the probability that the Best Buy stock rises (event B) is 34.5%. Write each answer as a decimal accurate to four decimal places.

a. The probability that either event A or event B occur if these two events are independent:   

b. The probability that event B does not occur: Correct  

c. The probability that both event A and event B occur if these two events are independent: Correct  

d. The probability that either event A or event B occurs, if these two events are dependent and the probability that both occur is 24.4%:   

e. The probability that event A does not occur, and event B does occur, if these two events are independent:

Answer 1

Hi Lakotah,

a. Formula for this is:

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

Now, recall that for independent events:

P(A and B) = P(A) * P(B)

Now, let's plug in our values from the problem:

P(A)= 0.464

P(B)= 0.345

P(A and B)= (0.464*0.345)

I will leave that multiplication and the subsequent calculation to you. Plug those values into your initial formula:

P(A or B) = P(A) + P(B) - P(A and B) to find probability that either stock rises.

b. Use the Complement Rule aka the "One Minus Trick:"

P(A^C)= 1 - P(A)

A^C= A's complement i.e. not A

You were essentially asked for B's complement, so compute:

P(B^C)= 1 - P(B); P(B) = 0.345 and you will have your probability.

c. This is the multiplication rule for independent events. For two events A and B:

P(A and B) = P(A) * P(B)

P(A)= 0.464

P(B)= 0.345

P(A and B)= (0.464*0.345)

I will leave this calculation to you. Once you multiply, you will have the probability that both stocks rise.

d. Use the general addition rule, as we did in part A:

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

Now, you were given that these events were dependent, and that the probability of both occurring together is 24.4%. So:

P(A)= 0.464

P(B)= 0.345

P(A and B)= 0.244

Plug those values into the formula above for the probability that either stock rises given those conditions.

e. This is a two-step problem. It requires the Complement Rule and the Multiplication Rule for Independent Events.

P(A^C)= 1 - P(A); P(A)= 0.464

P(A^C)= 1 - 0.464= 0.536

We want the probability of A's complement and B occurring together, and we know they are independent, so:

P(A^C and B)= P(A^C) * P(B)

P(A^C)= 0.536

P(B)= 0.345

Do that multiplication, and you will have the probability that Best Buy's stock rises without Aramark's stock rising. I hope this helps.