Rob has 10 white, 8 red, and 6 blue socks in his drawer. If he selects socks from the drawer randomly, without looking, what is the least number of socks Rob must select to guarantee that he has removed a pair of white socks?

The least number of socks that rob can remove to guarantee he removed a pair of white socks without looking is15 socks

Answered by Jazzy04 | 2024-06-10

Rob must select 16 socks to guarantee that he has at least one pair of white socks, considering the worst-case scenario where he picks all other colors first.

The question asks about the minimum number of socks Rob must select randomly from a drawer containing different numbers of white, red, and blue socks to ensure he has a pair of white socks. There are 10 white, 8 red, and 6 blue socks in total. To guarantee a pair of white socks, we must consider the worst-case scenario where Rob might pick socks of all other colors first. Rob could select up to 8 red and 6 blue socks without getting any white socks.
After this, any additional socks picked have to be white since only white socks remain in the drawer. So, to guarantee at least one pair of white socks, Rob must pick 8 (red) + 6 (blue) + 1 (white) = 15 socks. However, since we want a pair, we need to add one more white sock to the total, which brings us to 16 socks. Selecting 16 socks guarantees at least one pair of white socks.

Answered by qwarrow | 2024-06-24

Rob must select at least 16 socks to guarantee that he has removed a pair of white socks. This accounts for the possibility of drawing all the non-white socks first. Hence, the calculation shows he needs to pick 16 socks in total.
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Answered by Jazzy04 | 2024-10-12