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14.Probability
hard
A coin is tossed $3$ times by $2$ persons. What is the probability that both get equal number of heads
A
$\frac{3}{8}$
B
$\frac{1}{9}$
C
$\frac{5}{{16}}$
D
None of these
Solution
(c) The condition will be satisfied, if both get $0,\,\,1,\,\,2$ or $3$ heads.
$\therefore $ Either $0$ head by $A$ and $0$ head by $B$
or $1$ head by $A$ and $1$ head by $B$
or $2$ head by $A$ and $2$ head by $B$
or $3$ head by $A$ and $3$ head by $B$
$\therefore $ Required probability
$ = \left[ {\frac{1}{8} \times \frac{1}{8} + \frac{3}{8} \times \frac{3}{8} + \frac{3}{8} \times \frac{3}{8} + \frac{1}{8} \times \frac{1}{8}} \right] = \frac{5}{{16}}$.
Standard 11
Mathematics
