Question

What is the probability that the total of two dice is greater than 9, given that the first die is a 5? Give your answer as a fraction in simplest form.

Answer 1

Let A = first die is 5

Let B = total of two dice is greater than 9

`\text{P(A)}= (1)/(6)`

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Possible outcomes for A and B : {(5,5), (5,6)}

`\text{P(A and B)}=(2)/(36) =(1)/(18)`

`\text{P}\text{(B}|\text{A})=\frac{\text{P}(\text{A}\cap \text{B})}{\text{P(A)}}`

`=(1)/(18) *6= (1)/(3)`