10 coins are tossed. What is the probability | vedclass

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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?

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