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The faces of a die bear number 0,1,2,3,4...

The faces of a die bear number 0,1,2,3,4,5.
If the die is rolled twice, then find the probability that the product of the digits on the upper face is zero.

Text Solution

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The correct Answer is:
The probability that the product of the digits on the upper face is zero is `(11)/(36).`
The die is rolled twice.
`therefore "the sample space"`
`S={(0,0),(0,1),(0,2),(0,3),(0,4),(0,5),`
`(1,0),(1,2),(1,3),(1,4),(1,5),`
`(2,0),(2,1),(2,2),(2,3),(2,4),(2,5),`
`(3,0),(3,1),(3,2),(3,3),(3,4),(3,5),`
`(4,0),(4,1),(4,2),(4,3),(4,4),(4,5),`
`(5,0),(5,1),(5,2),(5,3),(5,4),(5,5)},`
`thereforen(S)=36`
Let A be the event that the product of the digits on the upper face is zero.
Then A= `{0,0),(0,1),(0,2),(0,3),(0,4),(0,5),`
`(1,0),(2,0),(3,0),(4,0),(5,0)}`
`thereforen(A)=11`
`P(A)=(n(A))/(n(S))" "thereforeP(A)=(11)/(36).`
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