a bag contain 6 tennis balls and 8 cricket balls three balls are randomly drawn from the bag what is the probability that at least one of the drawn balls I'd cricket ball?
Answers
Given : a bag contain 6 tennis balls and 8 cricket balls
three balls are randomly drawn from the bag
To Find : what is the probability that at least one of the drawn balls be cricket ball?
Solution:
Tennis Balls = 6
Cricket Balls = 8
Total = 6 + 8 = 14
3 balls are randomly drawn
can be drawn in ways = ¹⁴C₃ = 364
probability that at least one of the drawn balls be cricket ball
= 1 cricket ball + 2 cricket ball , 3 cricket balls
1 cricket ball ways = ⁸C₁.⁶C₂ = 8 * 15 = 120
2 cricket ball ways = ⁸C₂.⁶C₁ = 28 * 6 = 168
3 cricket ball ways = ⁸C₃.⁶C₀ = 56
Total Ways = 120 + 168 + 56
= 344
Probability = 344/364
= 86/91
= 0.945
Another way
1 - probability of 0 cricket ball
0 cricket ball = ⁸C₀.⁶C₃ = 20
Hence 1 - 20/364 = 344/364
= 86/91
= 0.945
probability that at least one of the drawn balls be cricket ball = 86/91
= 0.945
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