Final answer:
The probability that two of the eight digital cameras shipped to Cutler Electronics are defective is approximately 0.00989, or 0.989%.
Step-by-step explanation:
To calculate the probability that two of the eight digital cameras shipped to Cutler Electronics are defective, we can use the hypergeometric distribution. The hypergeometric distribution helps us determine the probability of a certain number of successes in a sample taken without replacement from a finite population, which in this case is the batch of digital cameras.
Firstly, we know there are 36 cameras in total with 7 defective ones. Cutler Electronics received 8 of these. We are looking to find the probability of receiving exactly 2 defective cameras out of the 8.
The hypergeometric probability is given by the formula:
P(X = k) = [(C(good, sample - k)) * (C(defective, k))] / C(total, sample)
Where: C(n, k) is the combination of n things taken k at a time.
Plugging the numbers into the formula, we have:
P(X = 2) = [(C(29, 6)) * (C(7, 2))] / C(36, 8)
Calculating the combinations, we get:
P(X = 2) = [(142506) * (21)] / 30260340 = 299226 / 30260340 ≈ 0.00989
Therefore, the probability that exactly two of the cameras shipped to Cutler Electronics are defective is approximately 0.00989, or 0.989%.