question archive 1a) You work part-time in an ice cream shop
1a) You work part-time in an ice cream shop
Subject:StatisticsPrice:2.84 Bought7
1a) You work part-time in an ice cream shop. You begin to take note of which ice cream flavors the customers who showed up today ordered. Out of the three flavors your shop offers, vanilla was chose by 9 customers, and raspberry by 4 customers. The third flavor remains untouched. Based on this observation, what is the probability that, of the next three customers, the first two will choose vanilla and the third one will choose raspberry?
(only round final answer to 2 decimal places, do not round intermediate numbers)
b) A robotic arm reaches into a box of manufactured parts and picks them out one by one for inspection. Once the item is inspected, if it is a defective it is discarded and if it passes the inspection, it is put on a conveyor belt and sent for further processing. Once the robotic arm either discards a part or puts one on the conveyor belt for further processing, it reaches into the box for the next part. A new box arrives and there are 55 parts in it. We know that this box contains 3 defective parts. what is the probability that the robotic arm will retrieve a defective part on the first time, but not on the second and third times it reaches into the box?
(express probability as a decimal number rounded to 2 decimal places)
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a) 0.15
b) 0.05
Step-by-step explanation
Based on the observation, P(v) = 9/13 (probability that any given customer will pick vanilla flavor), and P(r) = 4/13 (probability that any given customer will pick raspberry flavor)
Since the probabilities are independent of each other and constant, then it means, we can multiply the individual probabilities to find the probability of the combined event.
P(v, v, r) = P(v)·P(v)·P(r) = (9/13)·(9/13)·(4/13) = 0.1474738 ≈ 0.15 (rounded to 2 decimal points)
b) This part is a bit different than the previous part because the probabilities are not independent. But we can still solve by multiplying, only if we are careful about the changing probabilities. Let "d" represent a defective part, and "n" represent a non-defective part:
P(d,n,n) = (3/55)·(52/54)·(51/53) = 0.0505431675 ≈ 0.05 (rounded to decimal places)
Note : Please notice the diminishing denominator after (3/55). That is because once the defective part is picked, it is discareded, and there are 54 parts left in the box. Similarly, after (52/54), once the non-defective part is picked, the number of non-defective parts for the next selection is 51, out of 53 remaining part. Hence (51/53)
