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# Probability

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Help I need the answer quick

My sock drawer contains two red socks, two white socks, and two blue socks.  For three days in a row, I pull out two socks out of my sock drawer at random.  What is the probability that I get matching socks on all three days?

Apr 6, 2023

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We must take into account both the possible outcomes for each day and the total number of outcomes in order to calculate the probability of receiving matching socks on all three days.

On the first day, we have the option of picking any one of the six socks. On the second draw, we have a chance of getting a sock that matches the first one, but since there are only five socks left, only one of them matches the first one.

Since there are only three socks remaining, and only one of them matches the first sock, we can select one of the remaining four socks on the second day. The probability of receiving a matching sock on the second draw is 1/3.

On the third day, we can choose one of the remaining two socks. Since there is only one sock that matches the first two socks, the probability of getting a matching sock on the second draw is 1.

As a result, the likelihood of receiving matching socks on each of the three days is:

The probability of receiving matching socks on all three days is 4/45, or approximately 0.089, because (6/6) * (1/5) * (4/6) * (1/3) * (2/6) *(1/1)=4/45

Apr 6, 2023