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 !)^

Monjur Alahi

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 !)^2)(1/2)^(2n)` b. `1-((2n !))/((n !)^2)` c. `1-((2n !))/((n !)^2)1/(4^n)^` d. none of these
A. `((2n!))/((n!)^(2))((1)/(2))^(2n)`
B. `1-((2n!))/((n!)^(2))`
C. `1-((2n!))/((n!)^(2))(1)/(4^(n))`
D. None of these


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

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))`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
A coin is tossed three times, consider the following events. A : No head appears, B: Exactly one head appears and C: Atleast two appear. Do they form

The sample space of the experiment is `S = {HHH,HHT,HTH,THH,HT T,THT,T TH,T T T}` `A = {T T T}` `B = {HT T, THT, T TH}` `C = {HHT, HTH,...

2 Answers 1 views
Let X represent the difference between a number of heads and the number of tails when a coin is tossed 6 times.

When a coin is tossed 6 times, the number of heads can be 0, 1, 2, 3, 4, 5, 6.  The corresponding number of tails will be 6, 5, 4, 3,...

2 Answers 1 views
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)`

2 Answers 1 views
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.

2 Answers 1 views
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`

2 Answers 1 views
A man alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in t

Correct Answer - A The probability of getting a head in a single toss of a coin is P = 1/2 (say). The probability of getting 5 or 6 in a...

2 Answers 1 views
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...

2 Answers 1 views
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`

2 Answers 1 views
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)`

2 Answers 1 views
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)`

2 Answers 1 views
X