2:Hoyda has 15 percent of the car market. If a random sample of 20 auto mobiles is conducted what is the probabilitity that (a) exactly one of the car was made by hoyda (b) atleast two of the car were made by hoyda.
I will be happy to critique your thinking.
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To find the probability in this scenario, we can use the concept of binomial probability.
(a) To find the probability that exactly one car was made by Hoyda in a random sample of 20 cars:
The probability of selecting a car made by Hoyda is 15%, which can be written as 0.15. Since there are 20 cars in the sample, the probability of selecting exactly one car made by Hoyda can be calculated using the binomial probability formula:
P(X = 1) = (n C x) * (p^x) * (q^(n-x))
Where:
P(X = 1) is the probability of selecting exactly one car made by Hoyda,
n is the number of trials (20 in this case),
x is the number of successes (1 in this case),
p is the probability of success (0.15 or 15%),
q is the probability of failure (1 - p).
Plugging all the values into the formula, we get:
P(X = 1) = (20 C 1) * (0.15^1) * (0.85^(20-1))
Using a combination formula, (20 C 1) = 20, so:
P(X = 1) = 20 * 0.15 * 0.85^19
Calculating this value will give you the probability that exactly one car was made by Hoyda in the sample.
(b) To find the probability that at least two cars were made by Hoyda in the random sample of 20 cars:
In this case, we need to find the probability of getting 2, 3, 4, ..., 20 cars made by Hoyda and add them all together.
P(at least two cars) = P(X = 2) + P(X = 3) + P(X = 4) + ... + P(X = 20)
To calculate this, follow the same formula for each individual probability as in part (a) and sum them up.
Note: If you have access to a graphing calculator, statistical software, or an online binomial probability calculator, you can enter the values directly and get the results.