8.
You have several fair dices. Which of the following event has the highest
probability?
A
A atleast 16 with 6 dice
B atleast 2 6's with 12 dice
C atleast 3 6's with 18 dice
D atleast 4 6's with 24 dice
Answers
Given : Several fair dices
To Find : Which of the following event has the highest probability?
A atleast 1 6 with 6 dice
B atleast 2 6's with 12 dice
C atleast 3 6's with 18 dice
D atleast 4 6's with 24 dice
Solution:
Probability of 6 = p = 1/6
probability of not 6 = q = 1 - p = 5/6
atleast 1 6 with 6 dice = 1 - zero time 6
= 1 - (5/6)⁶
= 0.665
atleast 2 6's with 12 dice
1 - zero time 6 - 1 time 6
= 1 - (5/6)¹² - ¹²C₁(1/6)¹(5/6)¹¹
= 1 - 0.112 - 0.269
= 0.619
atleast 3 6's with 18 dice
1 - zero time 6 - 1 time 6 - 2 time 6
= 1 - (5/6)¹⁸ - ¹⁸C₁(1/6)¹(5/6)¹⁷ - ¹⁸C₂(1/6)²(5/6)¹⁶
= 1 - 0.0376 - 0.1352 - 0.2298
= 0.597
Similarly find
atleast 4 6's with 24 dice
1 - zero time 6 - 1 time 6 - 2 time 6 - 3 time 6
Hence atleast 1 6 with 6 dice has maximum probability in these
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