The probability that a voting-age adult in 2004 voted in the presidential election was 0.57. Five voting-age adults in 2004 were randomly selected. Find the probability that exactly 2 or the 5 adults voted in the presidential election.
To find the probability that exactly 2 out of 5 adults voted in the presidential election, we need to use the binomial probability formula.
The binomial probability formula is given by:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- n is the total number of trials
- p is the probability of success in a single trial
- C(n,k) is the number of combinations of n elements taken k at a time
In this case, we have:
- n = 5 (as there are 5 randomly selected voting-age adults)
- p = 0.57 (the probability that a voting-age adult in 2004 voted in the presidential election)
- k = 2 (we want to find the probability of exactly 2 adults voting)
First, let's calculate the number of combinations:
C(5, 2) = 5! / (2!(5-2)!) = 10
Now, we can plug in these values into the formula:
P(X=2) = 10 * (0.57)^2 * (1-0.57)^(5-2)
P(X=2) ≈ 0.3576 (rounded to four decimal places)
Therefore, the probability that exactly 2 out of the 5 adults voted in the presidential election is approximately 0.3576.