Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or...

Question

Question

Two dice are rolled repeatedly until the sum of the two numbers rolled is 10 or more.

a) What is the probability that exactly 5 rolls are needed? (Count each time you roll the dice as one roll).

b) What is the probability that more than 5 rolls are needed?

c) Find the expected number of rolls.

Answer 1

Answer #1

a)

here P(sum is 10 or more on pair of dice) =(P(10)+P(!1)+P(12)=(3/36)+(2/36)+(1/36) =6/36 =1/6

P( exactly 5 rolls are needed) =P(in first 4 rolls sum is less than 10 and on 5th 10 or more)

=(1-1/6)⁴*(1/6)=625/7776

b)

probability that more than 5 rolls are needed =P(first 5 roll all are below 10)=(5/6)⁶ =3125/7776

c)

expected number of rolls =1/p=1/(1/6)=6

Answer 2

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