a manufacturing process has a 70% meaning that 70% of the products are acceptable and 30% are defective. If three of the products are selected, find the probability that all of them are acceptable.
I have no idea what Ultra Instinct Shaggy is indicating.
.7^3 = .7 * .7 * .7 = ?
To find the probability that all three selected products are acceptable, we need to first understand that the probability of selecting an acceptable product is 70%. This means that the probability of selecting a defective product is 30%.
Now, let's calculate the probability step by step:
1. Calculate the probability of selecting an acceptable product on the first draw: Since the probability of selecting an acceptable product is 70%, the probability of selecting an acceptable product on the first draw is 70% or 0.7.
2. Calculate the probability of selecting an acceptable product on the second draw: Since the first selected product is not replaced, the number of acceptable products and the total number of products decrease. The probability of selecting an acceptable product on the second draw is now 69% (70% of the remaining acceptable products) or 0.69.
3. Calculate the probability of selecting an acceptable product on the third draw: Similar to the second draw, the probability of selecting an acceptable product on the third draw is now 68% (70% of the remaining acceptable products) or 0.68.
To find the probability that all three selected products are acceptable, we multiply the probabilities of each draw together since they are independent events:
0.7 (probability of the first draw being acceptable) × 0.69 (probability of the second draw being acceptable) × 0.68 (probability of the third draw being acceptable) = 0.32412.
Therefore, the probability that all three selected products are acceptable is approximately 0.32412 or 32.412%.