Two temperature readings both low

Question

Two independent readings are each equally likely to be anywhere between 0 and 20 (a uniform draw), and neither affects the other. What is the probability that both readings come out below 15?

Accepted Answer

Handle one reading first. For a single uniform value on 0 to 20, the chance of being below 15 is the proportion of the range below 15: P(	ext{one reading} < 15) = \frac{15}{20} = \frac34. Because the two readings are independent, the chance they are both below 15 is the product: P(	ext{both} < 15) = \left(\frac34ight)^2 = \frac{9}{16} = 0.5625. This equals the probability that the larger of the two readings is below 15, since "both below" and "maximum below" are the same statement. Even though each reading alone stays under 15 three-quarters of the time, needing both to cooperate drops th…

Two temperature readings both low

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