GMAT questions are always carefully worded - and with Quant questions, it might help to think of the details of the question as 'restrictions' (that essentially 'limit' what you should be thinking about and the type of math that you might work through). 2 being the desired no of cases and 36 being total no of cases. So, the probability is 2 chances out of 5 that the one that occurred had 5: P=2/5. Notice here that the case of (6,2) is different from (2,6), and similarly the case of (5,3) is different from (3,5).įrom this five cases, only in two we have 5.
What combinations of two cards are possible to total 8? Ĭan anyone shed some light please ? Thank you Some answers say 2/5, but since the cards can be replaced, I think 2/5 may not be the correct answer. Once we list them out, there clearly only 2 options (of the 5) that fit what we're looking for. The "given" is that the sum is equal to 8, meaning that we don't actually have to calculate the probability of getting that sum. It's worth noting that you can actually avoid most of these steps entirely if you focus on the specific 'pairings' that the prompt asks about. Of those five options, only two of them include a '5', so the probability of pulling a 3-5 or a 5-3 = 2/36 Thus, the probability of getting a sum of eight = 5/36 Of those 36 pairings, there are only a five options that actually add up to 8: With 6 cards, there are (6)(6) = 36 possible pairs that can be drawn. Here's what that unnecessary math would look like: This question involves some basic Probability math, but you might end up doing some unnecessary math along the way. We're asked for the probability that one of the two cards drawn is a 5. We're told that the sum of the numbers on the cards is 8. We're told that six cards numbered from 1 to 6 are placed in an empty bowl one card is drawn at random and then put back into the bowl and then a second card is randomly drawn. that one of the 2 cards is 5 given their sum is 8
It means sum is 8 and one of the cards is numbered 5 P (B/A) = P (A and B) / P(A) Ī: event that sum of the numbers on the 2 cards is 8ī : event that one of the 2 cards is numbered 5įavorable outcomes = (2,6) (3,5) (5,3) (6,2) (4,4) The formula for conditional probability says something like. This is a conditional probability question. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5? First one card is drawn and then put back into the bowl then a second card is drawn. Six cards numbered from 1 to 6 are placed in an empty bowl.
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