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Need help with probability

 

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?

 Mar 5, 2023
 #1
avatar+195 
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There are a total of 6 socks in the drawer, so the number of ways to choose 2 socks at random is (6 C 2) = 15. 

To find the probability of getting matching socks on any given day, we can count the number of ways to choose 2 socks of the same color, and divide by the total number of ways to choose 2 socks. 

There are 3 ways to choose 2 red socks, 3 ways to choose 2 white socks, and 3 ways to choose 2 blue socks. So the total number of ways to get matching socks on any given day is 3 + 3 + 3 = 9. 

Therefore, the probability of getting matching socks on any given day is 9/15 = 3/5. 

To find the probability of getting matching socks on all three days, we can use the multiplication rule of probability. That is, the probability of two independent events A and B both occurring is the product of their individual probabilities:

P(A and B) = P(A) × P(B)

In this case, we want the probability of getting matching socks on all three days, which are independent events. So the probability is:

P(getting matching socks on all three days) = (3/5) × (3/5) × (3/5) = 27/125

Therefore, the probability of getting matching socks on all three days is 27/125.

 Mar 5, 2023
 #2
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Justin:

 

1 - To get a matching pair of any of the 3 colors, you have:

2 / 6  x  1 / 5 = 2 / 30

But, you have 3 matching pairs. Therefore:

3  x  2 / 30 = 6 / 30 = 1 / 5 - probability of getting a matching pair on day 1

 

2 - On day 2, you would go through exactly the same procedure all over again, which means:

The probability is exactly the same as day 1 = 1 / 5

 

3 - On day 3, exactly the same = 1 / 5

 

4 - So, to get a matching pair 3 days in a row, you have:

The probability = (1 / 5)^3 = 1 / 125

 Mar 5, 2023
 #3
avatar+195 
0

Yes, your solution is correct. The probability of getting a matching pair of any of the 3 colors on day 1 is indeed 1/5, and this probability remains the same for day 2 and day 3. Therefore, the probability of getting a matching pair 3 days in a row is (1/5)^3, which is 1/125. Well done!

Justingavriel1233  Mar 5, 2023

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