Three vendors were asked to supply a very high precision component. The respective probabilities or their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one component the probability that out of total three components supplied by the vendors, at least one will meet the design specification is::
Question
Three vendors were asked to supply a very high precision component. The respective probabilities or their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one component the probability that out of total three components supplied by the vendors, at least one will meet the design specification is::
Solution
To solve this problem, we first need to understand that the probability of at least one event happening is equal to 1 minus the probability of none of the events happening.
Step 1: Identify the probabilities of each vendor meeting the design specifications. These are given as 0.8, 0.7, and 0.5 for vendors 1, 2, and 3 respectively.
Step 2: Calculate the probability of each vendor not meeting the design specifications. This is done by subtracting the probability of success from 1. So, for vendor 1 it's 1 - 0.8 = 0.2, for vendor 2 it's 1 - 0.7 = 0.3, and for vendor 3 it's 1 - 0.5 = 0.5.
Step 3: Calculate the probability of none of the vendors meeting the design specifications. This is done by multiplying the probabilities calculated in step 2. So, it's 0.2 * 0.3 * 0.5 = 0.03.
Step 4: Calculate the probability of at least one vendor meeting the design specifications. This is done by subtracting the probability calculated in step 3 from 1. So, it's 1 - 0.03 = 0.97.
So, the probability that out of the total three components supplied by the vendors, at least one will meet the design specification is 0.97 or 97%.
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