Probability Q

[jfranco23]

If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

[Stuart@KaplanGMAT]

If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

Super-horrible question! What's the source?

Problem (1): the question makes no sense.

When we have discrete probabilities (i.e. not ranges), it makes no sense to say "the greatest value for the probability" - there's going to be an exact answer to the question. If we had been given ranges of probability for each event, then the question would make sense.

Problem (2): the correct answer isn't among the choices.

The probability of two discrete independent events not occuring is simply:

Prob(event 1 not occuring) * Prob(event 2 not occuring)

In this question:

(1 - .54) (1 - .68) = (.46)(.32) = less than .22, the smallest answer. Therefore, the answer is:

(f) this question sucks

[jfranco23]

Jajaja, thanks Stuart, that is what I was thinking.

I did not understand the question when I read it, but after I made it as you say with the discrete probability of two discrete independent events.

[Cumulonimbus]

If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

Super-horrible question! What's the source?

Problem (1): the question makes no sense.

When we have discrete probabilities (i.e. not ranges), it makes no sense to say "the greatest value for the probability" - there's going to be an exact answer to the question. If we had been given ranges of probability for each event, then the question would make sense.

Problem (2): the correct answer isn't among the choices.

The probability of two discrete independent events not occuring is simply:

Prob(event 1 not occuring) * Prob(event 2 not occuring)

In this question:

(1 - .54) (1 - .68) = (.46)(.32) = less than .22, the smallest answer. Therefore, the answer is:

(f) this question sucks

Hi Stuart,

It is of some relief when someone like you says that this a horrible question. But this is from GMAT Prep. So dosen't matter how horrible it is.

I got the answer 0.15 not among among the answer choices...just guess as E.

[GMATGuruNY]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these 2 events will occur?
A) 0.22
B) 0.32
C) 0.37
D) 0.46
E) 0.63

We want to make it AS HARD AS POSSIBLE for A and/or B to occur.
Strategy:
Make one of the probabilities DEPENDENT on the other.
In other words, make it so that one of the events can't happen UNLESS the other event happens.

Let's rephrase the problem so that one of the probabilities is more clearly dependent on the other.
Since the non-dependent event does NOT require the other event -- making it EASIER for the non-dependent event to happen -- the non-dependent event must have the GREATER of the two probabilities.

Let B = John buys a lottery ticket.
P(B) = 0.68.
Let A = John wins the lottery.
P(A) = 0.54.
Here, the probability of A is clearly dependent on the probability of B: John can win the lottery only if he first buys a ticket.
Question rephrased:

If the probability that John wins the lottery is 0.54, and the probability that John buys a lottery ticket is 0.68, what is the greatest possible value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

If John DOESN'T buy a lottery ticket, then NEITHER event (buying a ticket, winning the lottery) occurs.
P(John doesn't buy a lottery ticket) = 1 - 0.68 = 0.32.

The correct answer is B.