A fair coin is tossed until one of the two sides occurs twice in a row. The probability that the number of tosses required is even is
A. `1//3`
B. `2//3`
C. `1//4`
D. `3//4`
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)`
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
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 - 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...