Question

You have four socks in your drawer, 2 blue and 2 brown. You get up early in the morning while it's dark, reach into your drawer, and grab two socks without looking. What is the probability that the socks are the same color? (Hint: If you take one sock first, what's the probability the second sock matches it?) If instead there are 13 blue and 13 brown socks, what is the probability that the socks you choose are the same color? (please write as a fraction.) first case ____________second case _____________

Answer 1

Answer:

First Case: 1/3

Second Case: 12/25

Step-by-step explanation:

The first case

Number of Blue Socks: 2

Number of Brown Socks: 2

Note that the first sock is guaranteed to be of the same color as those chosen. It is the only second sock that has to match the color of the first sock

Probability of picking socks of same colour = Probability of picking 2 blue socks or Probability of 2 brown socks

Mathematically,

P(Same Color) = P(Blue Socks) * P(Brown Socks)

P(Blue Socks) = P(1st blue socks) * P(2nd blue socks)

P(Blue Socks) = 2/4 * 1/3 = 1/6

P(Brown Socks) = P(1st brown socks) * P(2nd brown socks)

P(Brown Socks) = 2/4 * 1/3 = 1/6

P(Same Color) = P(Blue Socks) * P(Brown Socks)

P(Same Color) = 1/6 + 1/6

P(Same Color) = 1/3

The second case

Number of Blue Socks: 13

Number of Brown Socks: 13

Note that the first sock is guaranteed to be of the same color as those chosen. It is the only second sock that has to match the color of the first sock

Probability of picking socks of same colour = Probability of picking 2 blue socks or Probability of 2 brown socks

Mathematically,

P(Same Color) = P(Blue Socks) * P(Brown Socks)

P(Blue Socks) = P(1st blue socks) * P(2nd blue socks)

P(Blue Socks) = 13/26 " 12/25 = 6/25

P(Brown Socks) = P(1st brown socks) * P(2nd brown socks)

P(Brown Socks) = 13/26 " 12/25 = 6/25

P(Same Color) = P(Blue Socks) * P(Brown Socks)

P(Same Color) = 6/25 + 6/25

P(Same Color) = 12/25