1.

b) A pair of dice is thrown and one die shows a four. The probability that theother die shows 5 is

Answer»

As there is nothing told about the dies , let us assume the dies are identical. So as one die has 6 faces viz. 1,2,3,4,5,6 , if we through two dies we have (6×6=)36 sample points.

n(S)=36

Let A be the event that one die results in 4.

Let B be the event that other die results in 5.

So, required probabiity=p(B|A)

We know ,p(B|A)=p(A intersection B)/p(A)

Now the event ‘A intersection B' has 1 sample point (4,5) [as dies are identical, the points (5,4) & (4,5) ,aren't considered as different sample points].

So, p(A intersection B)=1/36

Again, the event A has 6 sample points in its sample space and 1 point in favourable case. So, p(A)=1/6

So,p(B|A)=(1/36)÷(1/6)=1/6


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