Question

A die is thrown $7$ times. The chance that an odd number turns up exactly 4 times, is given by

• A. $\frac{1}{128}$
• B. $\frac{35}{128}$
• C. $\frac{1}{2}$
• D. $\frac{31}{128}$

Answer 1

The correct option is B $\frac{35}{128}$

Die thrown $7$ times

No. of chances of odd number$=1,3,5=3$

Probability (odd no.)$=\frac{3}{6}=\frac{1}{2}$

p(odd)$=\frac{1}{2}$

$p=\frac{1}{2},q=1-p=1-\frac{1}{2}=\frac{1}{2}$

$p(x=4){=}^7{C}_4{p}^4{q}^3$

$=\frac{7!}{4!3!}\times {\left(\frac{1}{2}\right)}^7=\frac{7\times 6\times 5}{3\times 2}\left(\frac{1}{2^7}\right)$

$=\frac{35}{2^7}=\frac{35}{128}$