Question

two dice are rolled until a sum of either 5 or 7 occurs. estimate the probability that a 5 occurs first g

Answer 1

The correct answer is "
`(2)/(5)`". A further solution is provided below.

Explanation:

According to the question,

The probability of getting a 5 will be:

=
`(4)/(36)`

=
`(1)/(9)`

The probability of getting a 7 will be:

=
`(6)/(36)`

=
`(1)/(6)`

The probability of not a 5 nor a 7 will be:

=
`1-[(4)/(36) +(4)/(36) ]`

=
`(26)/(36)`

=
`(13)/(18)`

Now,

For roll of 2 dice,

⇒
`P=(1)/(9) +{(1)/(9)* ((13)/(18) ) }+{((1)/(9) )* ((13)/(18) )^2}+{(1)/(9)* ((13)/(18) )^3 }+...`

`=(1)/(9) [1+(13)/(18) +(13^2)/(18^2) +(13^3)/(18^3) +...]`

`=(1)/(9) [(1)/(1-(13)/(18) ) ]`

`=(1)/(9) [{(1)/((5)/(8) ) ]`

`=(2)/(5)`