A fair die is tossed repeatedly. `A` wins if if is 1 or 2 on two consecutive tosses and `B` wins if it is 3,4,5 or 6 on two consecutive tosses. The pr

Correct Answer - C Given that 5 and 6 have appeared on two of the dice, the sample space reduces to `6^(4) - 2 xx 5^(4) + 4^(4)` (inclusion-exclusion principle). Also,...

Since the trials are independent, so the probability that head appears on the fifth toss does not depend upon previous results of the tosses. Hence, required probability is equal to...

Let `E_(1)` be the event that the coin drawn is fair and `E_(2)` e the event that the coin drawn is biased. Therefore, `P(E_(1))=m/NandP(E_(2))=(N-m)/(N)` A is the event that on...

Correct Answer - D Player should get `(HT, HT, HT,...)orTH, TH,...)` at least 2n times. If the sequence starts from first place, then the probability is `1//2^(2n)` and if starts from...

Correct Answer - A `P(X=3)=((5)/(6))((5)/(6))1/6=25/216`

Correct Answer - B Given that `P(Xle2)=1/6+5/6xx1/6=11/36` Hence, the required probability is `1-(11//36)=25//36.`

Correct Answer - D For `Xge6,` the probability is `(5^(5))/(6^(6))+(5^(5))/(6^(7))+...oo=(5^(5))/(6^(6))((1)/(1-5//6))=((5)/(6))^(5)` For `Xgt3,` `(5^(3))/(6^(4))+(5^(4))/(6^(5))+(5^(5))/(6^(6))+...oo=((5)/(6))^(3)` Hence, the conditional probability is `((5//6)^(6))/((5//6)^(3))=25/36`

Correct Answer - B `(b)` `A={HH,HTHH,HTHTHH,…}` or `B={TT,THTT,THTHTT,…}` `P(A)=(1)/(2^(2))+(1)/(2^(4))+(1)/(2^(6))+.....=((1)/(4))/(1-(1)/(4))=(1)/(3)=P(B)` `:.` Required probability `=(1)/(3)+(1)/(3)=(2)/(3)`

Correct Answer - C `(c )` Let event `S to A` is getting `1` or `2` Event `F to B` is getting `3,4,5,6` `P(S)=P(1 or 2)=1//3` `P(F)=P(3 or 4 or 5...

Correct Answer - C `(c )` `E:` Event of getting on outcome `(n_(1), n_(2),n_(3))` such that `i^(n_(1))+i^(n_(2))+i^(n_(3))=1` `E_(1) : ` Event that fair die is thrown `E_(2) :` Event that biased...