five dices are thrown 150 times. The occurrences of an odd face are considered a success .tn how many throws do you expect 1)less than 4 successes 2)at least 3 succeses3)exactly one success
Answers
Given : 5 dices are thrown 150 times
The occurrences of an odd face are considered a success
To Find : how many throws do you expect
1)less than 4 successes
2)at least 3 success
3)exactly one success
Solution:
dice has 1 to 6 numbers
3 odd 1 , 3 , 5
probability of odd number p = 3/6 = 1/2
q = 1 - 1/2 = 1/2
p(x) = ⁿCₓpˣqⁿ⁻ˣ
n = 5
less than 4 successes
= 1 - P(4) - P(5)
= 1 - ⁵C₄(1/2)⁴(1/2)¹ - ⁵C₁(1/2)⁵(1/2)⁰
= 1 - 5/32 - 1/32
= 26/32
out of 150 = 150 * 26/32 = 121.87 = 122
in 122 throws expected less than 4 successes
at least 3 success
= P(3) + p(4) + P(5)
= ⁵C₃(1/2)³(1/2)² + ⁵C₄(1/2)⁴(1/2)¹ + ⁵C₁(1/2)⁵(1/2)⁰
= 10/32 + 5/32 + 1/32
= 16/32
= 1/2
150 * 1/2 = 75
in 75 throws expected at least 3 success
exactly one success
= P(1)
= ⁵C₁(1/2)¹(1/2)⁴
= 5/32
150 * 5/32 = 23.4 = 23
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