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Aleksandr-060686 [28]
3 years ago
12

exam p A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the dr

awer until a matching pair is obtained. Calculate the probability that the maximum number of draws is required.
Mathematics
1 answer:
Marta_Voda [28]3 years ago
5 0

Answer:

The probability that the maximum number of draws is required is 0.2286

Step-by-step explanation:

The probability that the maximum number of draws happens when you pick <em>different colors in the first four pick</em>.

Assume you picked one sock in the first draw. Its probability is 1, since you can draw any sock.

In the second draw, 7 socks left and you can draw all but the one which is the pair of the first draw. Then the probability is \frac{6}{7}

In the third draw, 6 socks left and you can draw one of the two pair colors which are not drawn yet. Its probability is \frac{4}{6}

In the forth draw, 5 socks left and only one pair color, which is not drawn. The probability of drawing one of this pair is \frac{2}{5}

In the fifth draw, whatever you draw, you would have one matching pair.

The probability combined is 1×\frac{6}{7} ×\frac{4}{6}× \frac{2}{5} ≈ 0.2286

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