Three-pair-of-socks-are-placed-in-a-box-If-two-socks-are-drawn-at-random-from-the-box-What-is-the-probability-a-of-drawing-a-match-pair-b-of-drawing-a-socks-for-the-left-and-right-feet-c-of-drawin

Question Number 87253 by peter frank last updated on 03/Apr/20

T h r e e p a i r o f s o c k s a r e

p l a c e d i n a b o x . I f t w o

s o c k s a r e d r a w n a t

r a n d o m f r o m t h e b o x

W h a t i s t h e p r o b a b i l i t y

(a) o f d r a w i n g a m a t c h

p a i r

(b) o f d r a w i n g a s o c k s

f o r t h e l e f t a n d r i g h t

f e e t

(c) o f d r a w i n g t w o s o c k s o f

t h e r i g h t f e e t

d) d r a w i n g t w o s o c k s o f

l e f t f e e t

(e) d r a w i n g s o c k s o f t h e

s a m e f e e t

Answered by malwaan last updated on 03/Apr/20

(a) \frac{1 + 1 + 1}{C_{2}^{6}} = \frac{3}{15} = \frac{1}{5}

(b) \frac{C_{1}^{3} \times C_{1}^{3}}{C_{2}^{6}} = \frac{3 \times 3}{15} = \frac{3}{5}

(c) \frac{C_{2}^{3}}{C_{2}^{6}} = \frac{3}{15} = \frac{1}{5}

(d) = \frac{1}{5} (== (c) ↰)

(e) \frac{C_{2}^{3} + C_{2}^{3}}{C_{2}^{6}} = \frac{3 + 3}{15} = \frac{6}{15} = \frac{2}{5}

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