Question

Assertion (A) : If $8$ coins are thrown simultaneously, then probability of occurrence of exactly $2$ tails is equal to the probability of occurrence of exactly $6$ tails.
Reason (R) : For binomial distribution, probability of $r$ success in $n$ trial is calculated as $P(X = r) = \,{}^nC_r p^r q^{n-r}$.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

$P(T) = P(H) = \frac{1}{2}$ (for one trial ), $ n = 8$
$\therefore P(X = r) = \,{}^8C_r(\frac{1}{2})^r(\frac{1}{2})^{8-r}$
$ = \,{}^8C_2(\frac{1}{2})^2(\frac{1}{2})^6 = \,{}^8C_6(\frac{1}{2})^6(\frac{1}{2})^2$.