stne wrote:
EMPOWERgmatRichC wrote:
Hi All,
For this question, we're given the probability that A occurs (0.4), but we're not given given the probability that B occurs. We are told that they're independent events though - that's important since it effects how the math has to be done.
Since we need to know the value of B to calculate the probability that EITHER A OR B OR BOTH will occur, we can solve this problem by TESTing THE ANSWERS. We're going to work our way down the list of values in the second column until we find a number that leads to one of the answers in the first column.
The easiest way to calculate the probability of "A or B or Both" is to actually calculate 1 - (not A)(not B).
So, starting in the second column...
If....
B = 0.10
1 - (not A)(not B) = 1 - (.6)(.9) = .46
That option does NOT exist in the first column
Eliminate this answer.
B = 0.25
1 - (not A)(not B) = 1 - (.6)(.75) = .55
That option DOES EXIST in the first column
This IS the correct set of answers.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Hi Rich ,
Thanks for the solution .
Just to better grasp the concept I was wondering how to arrive at the answer " The direct way ".
Probability of At least one event can be given by P(A) + P(B) +P(A)P(B) ..... either A or B or BOTH.
However when substituting the values I am getting 0.4+0.25 + 0.4*0.25= 0.75
what exactly am I forgetting here?
should I be subtracting P(A)P(B).
Very much appreciate your help thank you.
Yes, P(A or B) = P(A) + P(B) - P(A and B)
Think about why you subtract P(A and B). The concept is parallel to the sets concept. The Probability that both occur is counted twice - once in P(A) and then in P(B). So you subtract it out once to ensure no double counting.
Since A and B are independent events, P(A and B) = P(A) * P(B)
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A)*P(B)
P(A or B) = 0.4 + P(B) - 0.4*P(B)
P(A or B) = 0.4 + 0.6*P(B)
Now, look at what can be the value of P(A or B). It will be something more than 0.4. So try 0.5 for it.
doesn't work because 0.5 = 0.4 + 0.6*P(B) gives P(B) = .167 which is not one of the options for P(B).
Try 0.55 for P(A or B). You get P(B) = 0.25. It is there in the options.
So P(B) = 0.25 and P(A or B) = 0.55 is one of the many possible solutions.