This order was returned, did courier A deliver it?

Question

An online store shipped 400 orders: 240 went by courier A and 160 by courier B. Of courier A's 240 orders, 30 were returned. Of courier B's 160 orders, 50 were returned. You pick an order at random and it was returned. What is the probability courier A delivered it?

Accepted Answer

The clue "was returned" restricts you to returned orders, so count them first. - Courier A orders returned: 30. - Courier B orders returned: 50. Total returned orders: 30 + 50 = 80. Of those, courier A handled 30: P(	ext{courier A} \mid 	ext{returned}) = \frac{30}{80} = \frac{3}{8} = 0.375. Courier A shipped more orders overall, but its return rate is far lower, so it accounts for fewer than half of the returns. Takeaway. Among the conditioned group (returned orders), what matters is each courier's count of returns, which reflects both its volume and its return rate.

This order was returned, did courier A deliver it?

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