GMATSkilled wrote:
shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
Let's break this down
M will not occur = 0.8; M will occur = 0.2
R will not occur = 0.6; R will occur = 0.4
P(M or R) = P(M) + P(R) - P (M and R)
P(M or R) = 0.2 + 0.4 - 0
P(M or R) = 0.6 = 6/10 = 3/5
Note: Multiplying occurrence that will not occur + Multiplying occurrence that will occur is not equal to either event M or event R will occur
How can that formula be correct? What if the problem had said the probability that M will not occur is .5, and the probability that R will not occur is .5. Then according to your formula, you'd have:
P(M or R) = P(M) + P(R) - P(M and R)
P(M or R) = .5 + .5 - 0
P(M or R) = 1
So if two mutually exclusive events each have a 1/2 probability of occurring, then the probability of at least one of them occurring is 1 (100% of the time?) That doesn't make any sense to me, so I'm not exactly sure why that formula is what you're supposed to apply.
In a real-life scenario, that's like saying the Cardinals have a 40% chance to win the World Series, and the Yankees have a 20% chance to win, so the chance that one of them wins is 60% (since both of them cannot win)... Which doesn't make any sense. Again, what if you said the cardinals have an 80% chance to win and the Yankees have a 30% chance to win. So the chance that one of them wins is 110%?
The language in the question doesn't seem to suggest that either M or N must occur... In order to interpret the question the way the answer seems to, I would think the language would have to say something like "Out of 100 trials, M did not occur 80% of the time and N did not occur 60% of the time; if N and M never occurred on the same trial, what's the probability that a randomly selected trial will have M OR N occurring?" In that case, when you already have a list of events that happened, you could apply the formula P(M or R) = P(M) + P(R) - P(M and R)... Take it back to the 50% example, if you know that M occurred 50% of the time and N occurred 50% of the time, and M and N cannot happen, then you know that at least M or N had to happen every time. But when you're talking about the probability of a future event, as the problem seems to suggest, it doesn't make sense to just add the probabilities.
Can someone tell me if/how my reasoning is incorrect?