Question

A fair die will be rolled 11 times. What is the probability that an odd number is rolled exactly 7 times?

Answer 1

Answer:

0.161

Step-by-step explanation:

Given:

Number of trials, $n=11$

Consider the event of rolling odd number as success. There are 3 odd and 3 even numbers in a fair die.

So, probability of success, $p=0.5$

Probability of failure, $q=1-p=1-0.5=0.5$

Number of successes, $x=7$  

From Bernoulli's Theorem, the probability of $x$ successes in $n$ trials is given as,

$P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}$

Here, $x=7,n=11,p=0.5,q=0.5$

So, $P(X=7)=_{7}^{11}\textrm{C}(0.5)^{7}q^{11-7}\\ P(X=7)=0.161$

Therefore, the probability of getting an odd number exactly 7 times is 0.161.