A drawer contains 5 brown and 4 blue socks well mixed. A man reaches t

1.	A drawer contains 5 brown and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match ? (a) \(\frac{2}{9}\)(b) \(\frac{1}{3}\)(c) \(\frac{4}{9}\)(d) \(\frac{5}{9}\)
Answer» (c) \(\frac{4}{9}\) n(S) = Total number of waysin which 2 socks can be drawn out of 9 socks (5 brown and 4 blue socks) = ⁹C₂ = \(\frac{\|\underline9}{\|\underline7\|\underline2}\) = \(\frac{9\times8}{2}\) = 36 Let A : Event of drawing 2 socks of same colour ⇒ A = Drawing 2 brown socks out of 5 brown socks or Drawing 2 blue sock out of 4 blue socks ⇒ n(A) = ⁵C₂ + ⁴C₂= \(\frac{\|\underline5}{\|\underline3\|\underline2}\) + \(\frac{\|\underline4}{\|\underline2\|\underline2}\) = \(\frac{5\times4}{2}\) + \(\frac{4\times3}{2}\) = 10 + 6 = 16 ∴ Required probability P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{16}{36}\) = \(\frac{4}{9}\).

A drawer contains 5 brown and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match ? (a) \(\frac{2}{9}\)(b) \(\frac{1}{3}\)(c) \(\frac{4}{9}\)(d) \(\frac{5}{9}\)

Answer»

(c) \(\frac{4}{9}\)

n(S) = Total number of waysin which 2 socks can be drawn out of 9 socks (5 brown and 4 blue socks)

= ⁹C₂ = \(\frac{|\underline9}{|\underline7|\underline2}\) = \(\frac{9\times8}{2}\) = 36

Let A : Event of drawing 2 socks of same colour

⇒ A = Drawing 2 brown socks out of 5 brown socks or Drawing 2 blue sock out of 4 blue socks

⇒ n(A) = ⁵C₂ + ⁴C₂= \(\frac{|\underline5}{|\underline3|\underline2}\) + \(\frac{|\underline4}{|\underline2|\underline2}\) = \(\frac{5\times4}{2}\) + \(\frac{4\times3}{2}\) = 10 + 6 = 16

∴ Required probability P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{16}{36}\) = \(\frac{4}{9}\).

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