Let X represent the difference between a number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?
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A fair coin is tossed 4 times. Let X denote the number of heads obtained. Write down the probability distribution of X.
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} ∴...
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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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An unbiased normal coin is tossed `n` times. Let `E_1:` event that both heads and tails are present `n` tosses. `E_2:` event that the coin shows up he
`P(E_(1))=1-["P(all heads)+P(all tails")]` `=1-[(1)/(2^(n))+(1)/(2^(n))]=1-(1)/(2^(n-1))` `P(E_(2))=P("no head)+P(exactly one head")` `=(1)/(2^(n))+^(""n)C_(1).(1)/(2^(n))=(n)/(2^(n))` `P(E_(1)nnE_(2))=("exactly one head and"(n-1)till)` `=^(""n)C_(1).(1)/(2).(1)/(2^(n-1))=(n)/(2^(n))` If `E_(1)and E_(2)` are indipendent, then `P(E_(1)nnE_(2))=P(E_(1)).P(E_(2))` `implies(n)/(2^(n))=(1-(1)/(2^(n-1)))((n+1)/(2^(n)))` `impliesn=(1-(1)/(2^(n-1)))(n+1)`
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A coin is tossed three times in succession. If `E` is the event that there are at least two heads and `F` is the event in which first throw is a head,
Correct Answer - `3//4` `P(E)=4/8=1/2{because"favorable cases are"THH, HTH, HHT, HHH]` `P(F)=4/8=1/2[because"favorable cases are"HTH, HHT,HT T, HHH]` `P(EnnF)=3/8` `P(E//F)=(P(EnnF))/(P( F))=(3//8)/(1//2)=3/4`
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A coin is tossed three times. Event A: two heads appear Event B: last should be head Then identify whether events A and B are independent or not.
Correct Answer - Not independent `P(A)=3/8and P(B)=1/2` `P(A)P(B) =3/8xx1/2=3/16` `P(Annb)=2/8=1/4neP(A)P(B)` Hence, A and B aer not independent.
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A coin is tossed `2n` times. The chance that the number of times one gets head is not equal to the number of times one gets tails is `((2n !))/((n !)^
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))`
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A fair coin is tossed 100 times. The probability of getting tails 1, 3, .., 49 times is `1//2` b. `1//4` c. `1//8` d. `1//16`
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...
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An unbiased normal coin is tossed n times. Let `E_(1):` event that both heads and tails are present in n tosses. `E_(2):` event that the coin shows up
Correct Answer - 3 `P(E_(1))=1-[P ("all heads)=P(all tails")]` `=1-[(1)/(2^(n))+(1)/(2^(n))]=1-(1)/(2^(n-1))` `P(E_(2))=["P(no head)+P (exactly one head)"]` `=(1)/(2^(n))+""^(n)C_(1)xx(1)/(2^(n-1))=(n)/(2^(n))` If `E_(1) and E_(2)` are independent, then `(n)/(2^(n))(1-(1)/(2^(n-1)))((n+1)/(2^(n)))` `orn =(1-(1)/(2^(n-1)))(n+1)` `or n=n+1-(n+1)/(2^(n-1))` `or n+1=2^(n-1)` `or n=3`
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A fair coin is tossed `n` times. Let `a_(n)` denotes the number of cases in which no two heads occur consecutively. Then which of the following is not
Correct Answer - C `(c )` The cases for `a_(1){H,T}` i.e, `a_(1)=2` The cases for `a_(2){HT,TH,TT}`, `a_(2)=3` For `n ge 3` , if the first outcome is `H`, then next just...
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Three coins are tossed 100 times, and three heads one head occurred 14 times and head did not occur 23 times. Find the probability of getting more tha
Correct Answer - `(63)/(100)`
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