Find the probability that in five tosses of a fair die, a 3 will appear (i)twice (ii)at most once (iii)at least two times
Answers
Given : five tosses of a fair die
To Find : Probability that 3 will appear
(i)twice
(ii)at most once
(iii)at least two times
Solution:
n = 5
p = 1/6
q = 1 - p = 1 - 1/6 = 5/6
P(x) = ⁿCₓpˣqⁿ⁻ˣ
Probability that 3 will appear
(i)twice = P(2)
= ⁵C₂(1/6)²(5/6)³
= 10 * 5³ /6⁵
= 1250/7776
= 0.16075
at most once
= P(0) + P(1)
= ⁵C₀(1/6)⁰(5/6)⁵ + ⁵C₁(1/6)¹(5/6)⁴
= (5⁵ + 5⁵)/6⁵
= 6250/7776
= 0.803755
at least two times
= P(2) + P(3) + P(4) + P(5) + P(6)
= 1 - ( P(0) + P(1) )
= 1 - 0.803755
= 0.196245
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