Question

The random variable x represents the number of cars that failed among six that were tested for roadworthiness. Find the probability of getting three or more cars that fail among six cars tested.

a. 0.048
b. 0.736
c. 0.308
d. 0.952

Answer 1

The probability of getting three or more cars that fail among six cars tested is approximately 0.013061.

Step-by-step explanation:

To find the probability of getting three or more cars that fail among six cars tested, we can use the binomial probability formula: P(X >= k) = 1 - P(X < k). In this case, X represents the number of cars that fail, and k is 3. The formula can be used to calculate the probability of getting 3, 4, 5, or 6 cars that fail. Once we have the probabilities for each case, we can add them together to get the final probability.

Calculating the probabilities:

1. P(X = 3) = 6C3 * (0.1)^3 * (0.9)^3 = 0.012
2. P(X = 4) = 6C4 * (0.1)^4 * (0.9)^2 = 0.001
3. P(X = 5) = 6C5 * (0.1)^5 * (0.9)^1 = 0.00006
4. P(X = 6) = 6C6 * (0.1)^6 * (0.9)^0 = 0.000001

Adding all the probabilities together:

P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.012 + 0.001 + 0.00006 + 0.000001 = 0.013061

Therefore, the probability of getting three or more cars that fail among six cars tested is approximately 0.013061.