A coin is tossed 10 times. The probability of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a fair coin,the probability of getting a head in a single toss is $p = \frac{1}{2}$ and the probability of getting a tail is $q = 1 - p = \fra

Vedclass · Accepted Answer

$\frac{105}{512}$

Vedclass · Answer

(B) For a fair coin,the probability of getting a head in a single toss is $p = \frac{1}{2}$ and the probability of getting a tail is $q = 1 - p = \frac{1}{2}$.Since the coin is tossed $n = 10$ times,this follows a binomial distribution $B(n, p) = B(10, \frac{1}{2})$.The probability of getting exactly $k = 6$ heads is given by the formula $P(X = k) = {}^{n}C_k \cdot p^k \cdot q^{n-k}$.Substituting the values: $P(X = 6) = {}^{10}C_6 \cdot (\frac{1}{2})^6 \cdot (\frac{1}{2})^{10-6}$.$P(X = 6) = {}^{10}C_6 \cdot (\frac{1}{2})^{10}$.Calculating ${}^{10}C_6 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$.$P(X = 6) = 210 	imes \frac{1}{1024} = \frac{210}{1024} = \frac{105}{512}$.

$A$ coin is tossed $10$ times. The probability of getting exactly six heads is

Similar Questions

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random variable denoting the number of ace cards drawn,then the mean of the probability distribution of $X$ is

The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the $6$ members of the family,$5$ are sportspersons is

$A$ shooter can hit a given target with probability $\frac{1}{4}$. She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

$A$ 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 $n$ is equal to:

The probability of a person hitting a bird is $3/4$. If he tries $5$ times,what is the probability that he will not hit the bird even once (in $/1024$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module