A black and a red dice are rolled. (a)   Find the conditional probability of obtaining a sum greater than 9. Given that the black die resulted in a 5. (b)   Find the conditional probability of obtaining the sum 8? given that the red die resulted in a number less than 4.

Explanation

1. `E=` Event of 5 on black die.

`E={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}`
`P(E)=frac{6}{36}=frac{1}{6}`
`F=` Getting a sum greater than `9 .`
`F={(4,6),(5,5),(6,4)(5,6),(6,5),(6,6)}`
`Rightarrow E cap F={(5,5),(5,6)}`
`P(E cap F)=frac{2}{36}=frac{1}{18}`

Therefore the required probability

`P(E / F)=frac{P(E cap F)}{P(F)}=frac{frac{1}{18}}{frac{1}{6}}=frac{1}{3}`

2. `E=` Event of a number less than 4 on red die.

`E={(1,1),(1,2),(1,3),(2,1),(2,2),(2,3) `

`(3,1),(3,2),(3,3),(3,1),(3,2),(3,3) `

`(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)} `

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