10 coins are tossed. What is the probability | 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 tossing $10$ coins is $2^{10} = 1024$.The number of favorable outcomes for getting exactly $5$ heads is

Vedclass · Accepted Answer

$\frac{63}{256}$

Vedclass · Answer

(A) The total number of possible outcomes when tossing $10$ coins is $2^{10} = 1024$.The number of favorable outcomes for getting exactly $5$ heads is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$,where $n=10$ and $r=5$.${}^{10}C_{5} = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 252$.The required probability is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{252}{1024}$.Simplifying the fraction by dividing both numerator and denominator by $4$,we get $\frac{252 \div 4}{1024 \div 4} = \frac{63}{256}$.

$10$ coins are tossed. What is the probability that exactly $5$ heads appear?

Similar Questions

An $URN$ contains $6$ blue,$4$ red,$3$ green and $2$ yellow marbles. If four marbles are picked at random,what is the probability that one is yellow,two are red and one is blue?

Two numbers are selected at random from $1, 2, 3, \dots, 100$ and are multiplied. The probability, correct to two decimal places, that the product thus obtained is divisible by $3$ is:

$2$ unbiased dice are thrown. Find the probability that neither a doublet nor a total of $10$ will appear.

$A$ pair of dice is thrown. If $5$ appears on at least one of the dice,then the probability that the sum is $10$ or greater is:

Two dice are thrown. If the first die shows $5$,then the probability that the sum of the numbers on both dice is $8$ or more than $8$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module