A fair coin is tossed repeatedly. If tail appears on first four tosses, then find the probability of head appearing on fifth toss.
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Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail then throw a die. Find the conditional probabili
According to the equation, sample space `S = {(H,H),(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}` In the above set, there are 8 elementary events, but all are not equally likely. However, events (H,H) and (H,T) are...
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`Aa n dB` toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is `(3//4)^(50)` b. `(2/
Correct Answer - A For each toss, there are four choices: (i) A gets head, B gets head (ii) A gets tail, B gets head (iii) A gets head, B gets...
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A coin is tossed three times, where (i) A : head on third toss,B: heads on first two tosses (ii) A: at least two heads, B : at most two heads (iii) A
If a coin is tossed three times, then the sample S is `S={HHH,HHT, HTH, HT T ,THH,THT, T TH, T T T }` `thereforen(S)=8.` (i) `A={HHH, HTH, THH, T TH]`...
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A fair coin is tossed `n` times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value
Correct Answer - `n=14` According to question `""^(n)C_(6)((1)/(2))^(6)((1)/(2))^(n-6)=""^(n)C_(8)((1)/(2))^(8)((1)/(2))^(n-8)` `or ""^(n)C_(6)((1)/(2))^(n)=""^(n)C_(8)((1)/(2))^(n)` `or""^(n)C_(6)=""^(n)C_(8)=""^(n)C_(n-8)` `implies6=n-8orn=14`
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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 - B Let `P(S)=P(1 or 2)=1//3` `P(F)=P(3or4or5or6)=2//3` `P(A "wins")=P[(SS orSFSSorSFSFSSor..)or(FSSorFSFFSSor...)]` `=((1)/(9))/(1-(2)/(9))+((2)/(27))/(1-(2)/(9))` `= 1/9xx9/7+2/27xx9/7` `=1/7+2/21=(3+2)/(21)=5/21` P(A swining)`=5/21,` P(B winning)`=16/21`
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A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The probability that `X=3` equals
Correct Answer - A `P(X=3)=((5)/(6))((5)/(6))1/6=25/216`
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A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The probability that `ge3` equals
Correct Answer - B Given that `P(Xle2)=1/6+5/6xx1/6=11/36` Hence, the required probability is `1-(11//36)=25//36.`
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A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The conditional probability that `Xge6` given `Xgt
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`
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A biased coin with probability `p(0 lt plt 1)` of falling tails is tossed until a tail appears for the first time. If the probability that tail comes
Correct Answer - D `(d)` `P(T)=p`, `P(H)=1-p` `:.` Required probability `=P(T or HHT or HHHHT or ….)` `=p+(1-p)^(2)p+(1-p)^(4)+….` `=(p)/(1-(1-p)^(2))` `=(p)/(2p-p^(2))=(2)/(3)` `impliesp=(1)/(2)`
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A fair die is tossed repeatedly. A wins if it is `1` or `2` on two consecutive tosses and `B` wins if it is `3,4,5` or `6` on two consecutive tosses.
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...
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