Question

In your sock drawer you have 16 white socks, 7 black socks, 5 blue socks, and 2 yellow socks. What is the probability of picking a white sock, and probability of not picking a white sock, probability of picking a black or blue sock, and probability of picking a white and a yellow sock without replacement. Probability of picking at least 1 black sock when picking 6 socks? Is it ususal or unusual to pick a yellow sock?

Answer 1

16 white, 7 black, 5 blue, 2 yellow. total of 30 socks.

I). P(white) = 16/30 or 8/15

II). P(not white) = 14/30 or 7/15

III). P(black or blue) = (7 + 5)/30 or 2/5

IV). P(white and yellow w/o replacement) = P(1st white then yellow or 1st yellow then white)

P(white and yellow w/o replacement) = (16/30)(2/29) + (2/30)(16/29)

P(white and yellow w/o replacement) = (8/15)(2/29) + (1/15)(16/29)

P(white and yellow w/o replacement) = (16/435) + (16/435)

P(white and yellow w/o replacement) = 32/435


I did it the long way on purpose, but realize that you could have simply done

2[P(1st white then yellow)] = 2[P(1st yellow then white)] = 2(16/435) = 32/435


P(at least 1 black from 6) = (7C1)/(30C6)

\[=\frac{ 7 }{ 593 775 }\]
\[=\frac{ 1 }{ 84 825 }\]


P(yellow) = 2/30 or 1/15 ≈ 0.0667 so it is the least likely draw.

I hope this helps!

Answer 2

thank you so much i just do not get stats and have to pass with a C

Answer 3

You're welcome. Good Luck!

Answer 4

Don't I at least deserve a medal for that? lol