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Question

An unbiased cubic die marked with 1,2,2,3,3,3 is rolled 3 times. The probability of getting a total score of 4 or 6 is

A
16216
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B
50216
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C
60216
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D
none of these
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Solution

The correct option is B 50216
P(getting 1)=16P(getting 2)=26=13P(getting 3)=36=12
When the die is thrown 3 times a total of 4 or 6 can be obtained from following combinations
(1,1,2),(2,2,2),(1,2,3).
Let the event of getting 4 or 6 be called E.
Then P(E)=(3!2!)P(1)P(1)P(2)+P(2)P(2)P(2)+(3!)P(1)P(2)P(3)=3×16×16×13+13×13×13+(3!)×16×13×12=25108=50216

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