A survey of residents in a particular town indicated that 30% of the residents favour building a community centre and the others opposed it. Ten residents are randomly surveyed and asked if they favor the proposed new community centre.
What is the probability that no one favors the new community centre?
To find the probability that no one favors the new community centre, we can use the binomial probability formula:
P(X=k) = (n choose k) * (p^k) * (1-p)^(n-k)
Where:
- n = number of trials (10 residents surveyed)
- k = number of successes (0 residents favor the community centre)
- p = probability of success (30% favor community centre = 0.30)
- (n choose k) = combination formula or number of ways to choose k successes out of n trials
Plugging in the values:
P(X=0) = (10 choose 0) * (0.30^0) * (0.70^10)
P(X=0) = 1 * 1 * 0.0282475249
P(X=0) = 0.0282475249
So, the probability that no one favors the new community centre is approximately 0.028 or 2.8%.