To find the probability of selecting one red sock from the basket, and then selecting a second red sock without replacing the first, we follow these steps:
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Calculate the total number of socks:
- Red socks: 5
- White socks: 2
- Blue socks: 3
- Total socks = 5 (red) + 2 (white) + 3 (blue) = 10 socks.
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Find the probability of selecting the first red sock:
- Probability of selecting the first red sock = Number of red socks / Total number of socks = 5/10 = 1/2.
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Find the probability of selecting the second red sock after the first red sock has been removed:
- After removing one red sock, there are now 4 red socks left out of a total of 9 socks (since one sock has been removed).
- Probability of selecting the second red sock = Number of remaining red socks / Total remaining socks = 4/9.
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Calculate the combined probability:
- Combined probability = (Probability of first red sock) × (Probability of second red sock) = (5/10) × (4/9) = (1/2) × (4/9) = 4/18 = 2/9.
Thus, the probability of selecting one red sock and then a second red sock (without replacement) is \(\frac{2}{9}\).
The correct response is 2/9.