One drawer has 6 prs black, 3 prs gray socks. Another drawer has 11 wht, 6 colored scarves.?

Question

One drawer has 6 prs black, 3 prs gray socks. Another drawer has 11 wht, 6 colord scarves. In the dark I select 2 prs of socks, 1 scarf. What's the probability of selecting a pair of blk socks and a wht scarf?

Answer 1

Number of pairs of socks = 6 + 3 = 9.

Number of pairs of black socks = 6.

Number of pairs of gray socks = 3.

Probability of getting a pair of black socks when 2 pairs are selected = 6C₁* 8C₁/9C₂

= (6*8)/(9*8/2*1)

= 4/3.

Number of pairs of scraves = 11 + 6 = 17.

Probability of getting pair of white scrarf = 11C₁/17C₁ = 11/17.

Probability of getting pair of black socks and white scarf = (4/3) * (11/17) = 44/51.