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After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval

(b) At $8.30$, the call still hasn't arrived. What is the probability that it arrives in the next  $10$  minutes?

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Imagine a line with 120 time units and probability of marking a dot on it is uniformly distributed over that line.

Dot is the call by the representative and 120 are the minutes between $7$ PM and $9$ PM.

Now it is given in the question that at $8.30$ PM call is yet to arrive. So by this information we can concentrate all the probability of call arrival between 90 - 120 time units. $(8.30 - 9.00)$

$P(x<100 | x \geq90) =$$\large \frac{10}{30} = \frac{1}{3}$
by Boss (36.8k points)