a car insurance company has determined that 6% of all drivers were involved in a car accident last year,among the 12 drivers living on one particular street,3 were involved a car accident last year.if 12 drivers are randomly selected what is the probability of getting 3 or more who were involved in a car accident last year
To find the probability of getting 3 or more drivers who were involved in a car accident last year out of 12 randomly selected drivers, we can use the binomial probability formula.
The binomial probability formula is:
P(X = k) = (n choose 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 or drivers selected
- k is the number of successes (drivers involved in a car accident)
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials
- p is the probability of success (drivers involved in a car accident)
- (1-p) is the probability of failure
In this case:
- n = 12 (12 drivers are randomly selected)
- k = 3 or more (we want to find the probability of getting 3 or more drivers involved in a car accident)
- p = 0.06 (6% of all drivers were involved in a car accident last year)
Now, let's calculate the probability.
P(X = 3) = (12 choose 3) * 0.06^3 * (1-0.06)^(12-3)
P(X = 4) = (12 choose 4) * 0.06^4 * (1-0.06)^(12-4)
P(X = 5) = (12 choose 5) * 0.06^5 * (1-0.06)^(12-5)
P(X = 6) = (12 choose 6) * 0.06^6 * (1-0.06)^(12-6)
...
Finally, add up the probabilities for all values of X greater than or equal to 3:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + ...
This will give you the required probability.