If two coins are tossed 5 times,then the prob | vedclass

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(A) When two coins are tossed $5$ times,the total number of tosses is $2 	imes 5 = 10$ individual coin tosses.Let $n = 10$ be the total number of tri

Vedclass · Accepted Answer

$\frac{63}{256}$

Vedclass · Answer

(A) When two coins are tossed $5$ times,the total number of tosses is $2 	imes 5 = 10$ individual coin tosses.Let $n = 10$ be the total number of trials.The probability of getting a head in a single toss is $p = \frac{1}{2}$.The probability of getting a tail in a single toss is $q = 1 - p = \frac{1}{2}$.We want the probability of getting $5$ heads and $5$ tails in $10$ tosses.Using the binomial distribution formula $P(X = r) = ^nC_r p^r q^{n-r}$,where $r = 5$:$P(X = 5) = ^{10}C_5 \left(\frac{1}{2}ight)^5 \left(\frac{1}{2}ight)^5$$P(X = 5) = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1} 	imes \left(\frac{1}{2}ight)^{10}$$P(X = 5) = 252 	imes \frac{1}{1024} = \frac{252}{1024} = \frac{63}{256}$.

If two coins are tossed $5$ times,then the probability of getting $5$ heads and $5$ tails is

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