# In the most recent election, 30% of all eligible college students voted. If a random sample of 16...

## Question:

In the most recent election, {eq}30 {/eq}% of all eligible college students voted. If a random sample of {eq}16 {/eq} students were surveyed, find the probability that exactly half of them voted in the election?

## Binomial distribution

This is a typical example of a binomial distribution problem. We just have to guess the parameters from the given text description. This is widely use discreate distribution in probability. There is many aproximation theorems conected with it.

Since {eq}30\% {/eq} of all eligible college students voted, we conclude that the probability that randomly selected student has voted is equal to {eq}0.3 {/eq}. We recognize the binomail distribution {eq}\mathcal{B}(0.3,16) {/eq} with {eq}k=8 {/eq}

By the formula, we find

$${16 \choose 8}0.3^8 0.7^8 = {16 \choose 8}0.21^8 =12870\cdot 0.21^8 \approx 0.048678$$