Question

Assertion :STATEMENT-1 : The probability of getting a tail most of the time in 10 tosses of an unbiased coin is $\frac{1}{2}\{1-\frac{10!}{2^{10}5!5!}\}$ Reason: STATEMENT-2 : ${}^{2n}{C}_0{+}^{2n}{C}_1{+}^{2n}{C}_2+...{+}^{2n}{C}_n=2^{2n-1},nϵN$

• A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
• B. Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for Statement-1
• C. Statement-1 is True, Statement-2 is False
• D. Statement-1 is False, Statement-2 is True

Answer 1

The correct option is C Statement-1 is True, Statement-2 is False

Probability of getting a tail $6$ or $7$ or $8$ or $9$ or $10$ times $=\frac{C_6^{10}+C_7^{10}+C_8^{10}+C_9^{10}+C_{10}^{10}}{2^{10}}=\frac{210+120+45+10+1}{2^{10}}=\frac{386}{1024}=\frac{1}{2}[1-\frac{10!}{2^{10}5!5!}]$
Hence, statement $1$ is true.
${}^4{C}_0{+}^4{C}_1{+}^4{C}_2=11\ne 2^{4-1}$
Therefore, statement $2$ is false.