Probability question ... please explain

CFA Level I Quant
#1

Consider the following two independent events and corresponding probabilities: Event A) The probability that the auto demand will rise more than 5% during the coming year is 60%. Event B) The probability that the demand for cable television will rise more than 10% is 35%. The probability that neither events will occur is:

Select one: a. 74% b. 21% c. 26%

#2

Wouldn’t it just be P(not A) and P(not B) = 0.4 x 0.65 = 0.26

#3

My answer would be c. 26%.

My approach to the solution:

The probability of auto demand rising more than 5% during the coming year is 60%.

Therefore, the probability of auto demand NOT rising more than 5% during the coming year is = (100% - 60%) = 40% = 0.4

The probability that the demand for cable television will rise more than 10% is 35%.

Therefore, the probability that the demand for cable television will NOT rise more than 10% is = (100% - 35%) = 65% = 0.65

The probability that both these independent events will NOT occur = P(auto demand not rising) X P (cable demand not rising) = 0.4 X 0.65 = 0.26 = 26%

#4

http://www.youtube.com/watch?v=EndWGGSC23U&feature=youtu.be

This video nicely explain this question.

#5

Basically just multiply probabilities together. I use this whenever I’m tempted to play the lottery.

#6

I’m not sure if this is right but:

I gota answer C- 0.25

P(A: auto > 5%) = 0.6

P(B: cable>10%)=0.35

P(A: auto > 5% or B: cable>10%) = 0.6 + 0.36 - (0.6 x 0.35) = 0.95 - 0.21 = 0.74

P( NOT A: auto > 5% or B: cable>10%) = 1-0.74 = 0.26

is this the right way to think of this problem???

#7

Yes, yours is one of the right ways, but costs you more time. To be simple: P(~A) = 0.4 and P(~B) = 0.65 Therefore, P(~A and ~B) = 0.4 * 0.65 = 0.26 By the way, you made two typos: 1) 0.25 but not 26 on 2nd line, and, 2) 0.6 + 0.35 instead of 0.6 + 0.36 on 5th line.

#8

thanks mate, the other way is much easier!

oops yes my bad,

answer C = 0.26

and yes, P(A: auto > 5% or B: cable>10%)= 0.6+0.35- (0.6 x 0.35) = 0.95 - 0.21 = 0.74

#9

Just feel the intuition behind it before you answer the question. First calculate the probablitites that those events won’t occur. Those are 40% and 65% for A complement and B complement respectively. Then, see if there is a joint probability. Since these are independant events, there isn’t a joint probability. Therefore the answer is just the multiplication of the two probabilites of the complement of those events hapening. Therefore, the answer if 26% or C.

#10

Isn’t it incorrect to use the joint probablitiy there?

#11

Isn’t it incorrect to think that there is a joint probability there?

#12

Isn’t it incorrect to think that there is a joint probability there?

#13

Sorry for the double comment, I am still new here.

#14

Sorry for the double comment, I am still new here.

#15

why is it not correct to calculate p(A andB)= 0.21 and then p(non(Aand B)= 1 - 0.21 = 0.79?

#16

In this case you are looking for P(not(AorB)) not p(not(AB)). Therefore, once you get P(AandB) you need to use addition rule P(A or B)= P(A) + P(B)-P(AandB)= 0.60+0.35-0.21= 0.74. P(AorB)= 0.74 so P(not(AorB) = .026.

#17

Ana, you are right saying that p(not(A and B)) is 0.79. However, notice that based on the rules of logic not(A and B) = not(A) or not(B) whereas the question is asking about probability(not(A) and not(B)). Is this helpful?

#18

thank you cfageist and maratikus:) i’ll definitely remeber this trick