A fair coin is tossed 100 times. The probabil | vedclass

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

Question

(A) The total number of possible outcomes when a coin is tossed $100$ times is $2^{100}$.The number of ways to get tails an odd number of times is giv

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(A) The total number of possible outcomes when a coin is tossed $100$ times is $2^{100}$.The number of ways to get tails an odd number of times is given by the sum of combinations: $\binom{100}{1} + \binom{100}{3} + \dots + \binom{100}{99}$.Using the binomial identity $\sum_{k 	ext{ odd}} \binom{n}{k} = 2^{n-1}$,we have $\binom{100}{1} + \binom{100}{3} + \dots + \binom{100}{99} = 2^{100-1} = 2^{99}$.Therefore,the required probability is $\frac{2^{99}}{2^{100}} = \frac{1}{2}$.

$A$ fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

Similar Questions

If $12$ dice are thrown at a time,then the probability that a multiple of $3$ does not appear on any dice is

Let $9$ distinct balls be distributed among $4$ boxes,$B_{1}, B_{2}, B_{3}$ and $B_{4}$. If the probability that $B_{3}$ contains exactly $3$ balls is $k\left(\frac{3}{4}\right)^{9}$,then $k$ lies in the set:

The binomial distribution for which mean $= 6$ and variance $= 2$,is

$A$ die is thrown $6$ times. If 'getting an odd number' is a success,what is the probability of at least $5$ successes?

$A$ dice is thrown $10$ times. If getting an even number is considered as a success,then the probability of $4$ successes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module