In the two dice experiment, if A is the event of getting the sum of the numbers on dice as 11 and B is the event of getting a number other that 5 on the first die, find `P(A`and`B)` Are A and B independent events? OR Two dice are tossed. Find whether the following two events A and B are independent: `A={(x , y): x+y=11},B={(x , y): x!=5},w h e r e(x , y)` denote a typical sample point.

Explanation

Total outcomes `=6 times 6=36`

Number of outcomes favourable to E`=2. [i.e., (5,6),(6,5) ]`

Take F be the event that the number 5 does not appear on the first die.

Outcomes favourable to `F=30`

Now,` P(E)=frac236=frac118, P(F)=frac3036=frac56`


`P(E cap F)=frac136 neq frac118 times frac56=P(E) times P(F)`


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