Question

A contest consists of prediciting the results (win,draw or defeat) of 10 footballs matches. The probability that one entry contains at least 5 correct answers is

• A. $\frac{12585}{3^{10}}$
• B. $\frac{12385}{3^{10}}$
• C. $\frac{9335}{3^{10}}$
• D. $\frac{12096}{3^{10}}$

Answer 1

The correct option is D $\frac{12096}{3^{10}}$

P(correct)=$\frac{1}{3}$

P(wrong)=$\frac{2}{3}$

here $n=5$

P${=}^{10}{C}_5{\left(\frac{1}{3}\right)}^5{\left(\frac{2}{3}\right)}^5$

$=\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 2^5}{(5\times 4\times 3\times 2)(5\times 4\times 3\times 2)\times 3^5\times 3^5}$

$=\frac{252\times 2^5}{3^{10}}$

$=\frac{12096}{3^{10}}$