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 of `ndot`
When a fair coin is tossed 4 times then the sample space is
S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}
∴...
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
Let `p_(i)` denote the probability that out of 10 tosses, head occurs I times and no two heads occur consecutively. If is clear that `igt5.`
For I...
Correct Answer - C
The required probability is
1- probability of getting equal number of heads and tails
`=1-""^(2n)C_(n)((1)/(2))^(n)((1)/(2))^(2n-n)`
`=1-((2n)!)/((n!)^(2))xx(1)/(4^(n))`
Correct Answer - B
Let the probability of getting a tail in a single trial be `p=1//2.` The number of trials be n=100 and the number of trials in 100 trials...
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 )` `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...
