Question

There are six normal dice in a box, and one special die (which has sixes on two sides and ones on the remaining four sides). We randomly draw a die, and then roll it 10 times.

a) What is the probability that each number obtained will be a 1 or a 6?

b) What is the probability that we have chosen the special die, given that each number obtained was a 1 or a 6?

Answer 1

let N is normal dice and S is special dice

P(selecting N dice)=P(N)=6/7

P(selecting S dice)=1/7

let X is event of getting number 1 or 6

when we select normal dice then P(getting 6 or 1) =2/6 =1/3

so out of 10 rolling getting all number 1 or 6

here in this case P(X|N) =p=1/3

now

when we select special dice then

P(X=10 | S) =1 (as S have only 6 and 1)

a)

we have to find

P(X=10) =P(X=10|N)*P(N) +P(X=10|S)*P(S)

=0.000017*(6/7) +1*(1/7) =0.1429

b)

we have to find P(S|X=10)

now

=0.9993