Question

A die is thrown $7$ times. What is the chance that an odd number turns up exactly $4$ times?

• A. $\frac{1}{2}$
• B. $\frac{35}{128}$
• C. $\frac{37}{128}$
• D. $\frac{63}{128}$

Answer 1

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

P(odd)$=$P(even)$=$ $\frac{1}{2}$
Now considering that getting an odd number is a success.
Hence In 7 trials, getting exactly four odd numbers is
$={}^7{C}_4{\left(\frac{1}{2}\right)}^4.{\left(\frac{1}{2}\right)}^3$
$=\frac{{}^7{C}_4}{2^7}$
$=\frac{35}{128}$.