Question

Two unbiased dice arethrown.Find the probability that the aum of numbers shown is 7 and their product is 12​

Answer 1

Solution :

Here , two unbiased dice are thrown .

So , the required sample space comes out to be :

S € [ (1,1) , (1,2) , ....... , (1,6) , (2,1 ) ,. ....... ( 6,6 ) ]

Here, the cases when the numbers add to 7 are :

• (1,6) & (6,1)

• (2,5) & (5,2)

• (3,4) & (4,3)

Here , there is another condition , that the product of these numbers have to be 12.

Only two values , (3,4) and (4,3) satisfy this.

So, the required number of favourable cases turns out to be 2 .

There are a total of 36 cases ( sample space) .

Thus , the probability becomes :

=> 2/16

=> 1/18 .

This is the required answer .

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Answer 2

Answer in attachment......