MHT CET · Maths · Probability
15 coins are tossed, then the probability of getting 10 heads will be
- A \(\frac{511}{32768}\)
- B \(\frac{1001}{32768}\)
- C \(\frac{3003}{32768}\)
- D \(\frac{3005}{32768}\)
Answer & Solution
Correct Answer
(C) \(\frac{3003}{32768}\)
Step-by-step Solution
Detailed explanation
\(\therefore\) Required probability \(={ }^{15} C_{10}\left(\frac{1}{2}\right)^{10}\left(\frac{1}{2}\right)^{5}\)
\(={ }^{15} C_{5} \frac{1}{2^{15}}\)
\(=\frac{15 \times 14 \times 13 \times 12 \times 11}{5 \times 4 \times 3 \times 2 \times 1} \times \frac{1}{2^{15}}\)
\(=\frac{3003}{32768}\)
\(={ }^{15} C_{5} \frac{1}{2^{15}}\)
\(=\frac{15 \times 14 \times 13 \times 12 \times 11}{5 \times 4 \times 3 \times 2 \times 1} \times \frac{1}{2^{15}}\)
\(=\frac{3003}{32768}\)
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