ProbabilityHardBloom L3
Question
A fair die is tossed 16 times, then the probability of getting prime outcomes as many times in the first 8 throws as in the last 8 throws is equal to
Options
A.$\frac{\ ^{16}C_{8}}{2^{16}}$
B.$\frac{\ ^{15}C_{7}}{2^{16}}$
C.$\frac{\ ^{16}C_{8}}{2^{17}}$
D.$\frac{\ ^{15}C_{7}}{2^{17}}$
Solution
Sol. [Key Concept: Fair die tossed 16 times: probability of the stated outcome.]
Probability of getting prime outcome in any throw $= P(2,3,5) = \frac{3}{6} = \frac{1}{2}$
$$\begin{matrix} & \ \therefore\ P = \left( \frac{1}{2} \right)^{16}\left( \ ^{8}C_{0}^{2} + \ ^{8}C_{1}^{2} + \ ^{8}C_{2}^{2} + \ldots + \ ^{8}C_{8}^{2} \right) \\ & \ = \frac{\ ^{16}C_{8}}{2^{16}} \end{matrix}$$
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