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
