Question

A small voting district has 146 Republican voters and 78 Democrat voters. A random sample of 13 voters is drawn. What is the probability exactly 8 of the voters will be Republican?

Answer 1

To find the probability of exactly 8 Republican voters out of a sample of 13 voters, we can use the binomial probability formula.

Step-by-step explanation:

This question involves finding the probability of selecting exactly 8 Republican voters out of a random sample of 13 voters from a small voting district.

We can use the binomial probability formula to calculate this:

P(x=k) = (nCk) * p^k * (1-p)^(n-k)

Where:

• P(x=k) is the probability of getting exactly k successes
• n is the number of trials or sample size (13 in this case)
• k is the number of successes we are interested in (8 in this case)
• p is the probability of success (probability of selecting a Republican voter) which is 146 / (146 + 78) = 0.6515

Using the values above, we can plug them into the formula:

P(x=8) = (13C8) * (0.6515)^8 * (1-0.6515)^(13-8)

Simplifying this expression gives us the final probability value.