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CBSE Class 12-science Answered

A bag contains 5 white balls and 9 red balls. Three balls are drawn, without replacement, from the bag. What is the probability that at least one ball is white?

Asked by sachinkumarmishra1 | 27 Jan, 2020, 12:27: PM
Expert Answer
Total number of balls = 5 + 9 = 14
Total number of ways of drawing 3 balls without replacement = 14 x 13 x 12
There are three different possbilities of drawing 3 balls such that at least one ball is white
Case 1: 1 white 2 red
Number of ways = 5 x 9 x 8
Case 2: 2 white 1 red
Number of ways = 5 x 4 x 9
Case 3: 3 white 0 red
Number of ways = 5 x 4 x 3
T h e r e f o r e comma space p r o b a b i l i t y space o f space g e t t i n g space a t space l e a s t space 1 space w h i t e space b a l l space i s
P equals fraction numerator 5 cross times 9 cross times 8 over denominator 14 cross times 13 cross times 12 end fraction plus fraction numerator 5 cross times 4 cross times 9 over denominator 14 cross times 13 cross times 12 end fraction plus fraction numerator 5 cross times 4 cross times 3 over denominator 14 cross times 13 cross times 12 end fraction equals fraction numerator 360 plus 180 plus 120 over denominator 14 cross times 13 cross times 12 end fraction equals fraction numerator 660 over denominator 14 cross times 13 cross times 12 end fraction equals 55 over 182
Answered by Renu Varma | 29 Jan, 2020, 09:41: AM
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