16807, (C) 0.00243, (D) 0.15
2. The probability of winning a game is 0.3. Neil plays the game 5 times. What is the
probability that he wins the game at most 1 once?
(A) (B) (C),(D)
3. If mean and standard deviation of a Binomial Distribution are 8 and 2 respectively
Answers
Given : The probability of winning a game is 0.3.
Neil plays the game 5 times
To Find : probability that he wins the game at most 1 once
Solution:
The probability of winning a game is 0.3.
=> p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
n = 5
wins the game at most 1 once => x = 0 , 1
p(x) = ⁿCₓpˣqⁿ⁻ˣ
probability that he wins the game at most 1 once
= P(0) + P(1)
= ⁵C₀(0.3)⁰(0.7)⁵ + ⁵C₁(0.3)¹(0.7)⁴
= 0.16807 + 0.36015
= 0.52822
probability that he wins the game at most 1 once 0.52822
mean = np = 8
variance = npq
variance = standard deviation² = 2² = 4
npq = 4
=> 8q = 4
=> q = 1/2
p = 1 - q = 1/2
np = 8
=> n(1/2) = 8
=> n = 16
n = 16 , p = 1/2 q = 1/2
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