Challenging Probability problem 5

An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will

i) be 1, 2,3, 4, 5,6 in some order

ii) have a product which is an even number

iii) consists of exactly two 6’s and four odd numbers

Solution

dice prob

iii Alternative solution

6C2: 6 slots choose 2 slots to insert the two 6s. Remaining 4 slots automatically will be for the four odd numbers.
3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4
Probability = (6C2 x 3^4) / 6^6 = 5/192

 

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