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kati45 [8]
3 years ago
5

From a deck of five cards numbered 2, 4, 6, 8, and 10, respectively, a card is drawn at random and replaced. this is done three

times. what is the probability that the card numbered 2 was drawn exactly two times, given that the sum of the numbers on the three draws is 12?
Mathematics
1 answer:
Serga [27]3 years ago
3 0

Since the sum of the numbers on the three draws is 12, if we want the card numbered 2 to be drawn exactly two times, the third card can only be numbered 8. In fact, 2+2+8 = 12, and there are no other possibilities, unless you consider the various permutations of the terms.

So, we have three favourable cases: we can draw 2,2,8, or 2,8,2, or 8,2,2. This are the only three cases where the card numbered 2 is drawn exactly two times, and the sum of the number on the three draws is 12.

Now, the question is: we have three favourable cases over how many? Well, we have 5 possible outcomes with each draws, and the three draws are identical, because we replace the card we draw every time.

So, we have 5 possible outcomes for the first draw, 5 for the second and 5 for the third. This leads to a total of 5 \times 5 \times 5 = 5^3 = 125 possible triplets.

Once we know the "good" cases and the total number of possible cases, the probability is simply computed as

P = \cfrac{\text{number of favourable cases}}{\text{number of all possible cases}} = \cfrac{3}{125}

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