An unbiased cubical dice is thrown 5 times and the number appearing
on the uppermost face is noted. Then the probability that atmost two
times an even number appears is
A) 0.125
B) 03125
C) 0.25
D) 0. 5
Answers
Given : An unbiased cubical dice is thrown 5 times and the number appearing on the uppermost face is noted.
To Find : the probability that atmost two times an even number appears is
A) 0.125
B) 03125
C) 0.25
D) 0. 5
Solution:
Dice has 6 numbers 1 to 6
3 even numbers and 3 odd numbers
Probability of even number p = 3/6 = 1/2
Probability of not appearing even number q = 1 - p = 1 - 1/2 = 1/2
n = 5 dice thrown 5 times
p(x) = ⁿCₓpˣqⁿ⁻ˣ
atmost two times an even number appears
x= 0 , 1 , 2
probability that atmost two times an even number appears is
= P(0) + p(1) + P(2)
= ⁵C₀(1/2)⁰(1/2)⁵ + ⁵C₁(1/2)¹(1/2)⁴ + ⁵C₂(1/2)²(1/2)³
= 1/32 + 5/32 + 10/32
= 16/32
= 1/2
= 0.5
probability that atmost two times an even number appears is 0.5
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