Final answer:
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:
- P(X = 3) = 6C3 * (0.1)^3 * (0.9)^3 = 0.012
- P(X = 4) = 6C4 * (0.1)^4 * (0.9)^2 = 0.001
- P(X = 5) = 6C5 * (0.1)^5 * (0.9)^1 = 0.00006
- 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.