Given that 65% of people who purchase sports cars are men. If 10 sports car owners are randomly selected, find the probability that 6 are men.
evaluate
C(10,6) (.65)^6 (.35)^4
Where did you get the .35?
I don't understand?
percentage of sports car owner who are men = 65% or .65
so percentage of sport car owners who are NOT men = 35% or .35
Clearly to be able to do this type of question, you MUST have studied or
learned about Binomial Distribution probability
To find the probability that 6 out of 10 randomly selected sports car owners are men, we can use the binomial probability formula.
The binomial probability formula is given by:
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 number of trials
- k is the number of successes
- p is the probability of success for each trial
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials, and it is calculated as: (n choose k) = n! / (k! * (n - k)!)
In this case:
- n = 10 (number of trials)
- k = 6 (number of successes)
- p = 0.65 (probability of being a man)
Now we can calculate the probability using the formula:
P(X = 6) = (10 choose 6) * 0.65^6 * (1 - 0.65)^(10 - 6)
To calculate (10 choose 6):
(10 choose 6) = 10! / (6! * (10 - 6)!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Now we can substitute the values into the formula:
P(X = 6) = 210 * 0.65^6 * (1 - 0.65)^4
Calculate 0.65^6 = 0.2785390625 and (1 - 0.65)^4 = 0.06903125.
P(X = 6) = 210 * 0.2785390625 * 0.06903125
Calculate 210 * 0.2785390625 * 0.06903125 = 3.94653320313.
Therefore, the probability that exactly 6 out of 10 randomly selected sports car owners are men is approximately 0.3947 or 39.47%.