What is the probability that both suppliers deliver the material in 4 days? In other words, what is the probability that Supplier A delivers in 4 days, and Supplier B delivers in 4 days?

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BlackTom AI · Accepted Answer

Let's break down the problem and lay out what is needed to compute the probability.

- We are asked for the probability that both suppliers deliver in exactly 4 days, i.e., P(A = 4 and B = 4).
- If the delivery times of the two suppliers are independent, then the joint probability factors: P(A = 4 and B = 4) = P(A = 4) × P(B = 4).
- The given numerical answer is 0.1925. This value represents the product P(A = 4) × P(B = 4).

Now, to understand what this implies about the individual probabilities:
- If the two suppliers have identical delivery-time distributions, then P(A = 4) = P(B = 4) = p for some p. In that case, p × p = 0.1925, so p = sqrt(0.1925).
- Calculating sqrt(0.1925) gives approximately 0.439 (more precisely about 0.4389). This would mean each supplier has about a 43.9% chance of delivering in exactly 4 days, and together they'd have a 19.25% chance of both delivering in 4 days when independent.

If the two suppliers do not have identical distributions, you can still apply the same principle:
- Let pA = P(A = 4) and pB = P(B = 4).
- Then P(A = 4 and B = 4) = pA × pB = 0.1925.
- Without additional information about pA and pB, you cannot determine the exact individual probabilities from the product alone. You would need either the individual values or the distribution details to separate pA and pB.

Further considerations:
- If the delivery times are not independent, the product rule would not apply, and one would need the joint distribution or the correlation between A and B to compute P(A = 4 and B = 4).
- If there are multiple possible ways to achieve 0.1925 with pA and pB (e.g., pA = 0.5 and pB = 0.385, etc.), each pair would still satisfy pA × pB = 0.1925, but only the specific pair consistent with the given distributions would be correct for the scenario.

Summary: given the product 0.1925 and assuming independence, the product represents P(A = 4) × P(B = 4). If the two suppliers share the same distribution, each has P(4) ≈ 0.439, since 0.439 × 0.439 ≈ 0.1925. Otherwise, you would need additional information about the individual probabilities to determine pA and pB exactly.

COMM_V 190 101-104 2025W1 HW08.COMM190.2025.W1

What is the probability that both suppliers deliver the material in 4 days? In other words, what is the probability that Supplier A delivers in 4 days, and Supplier B delivers in 4 days?

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