Question

Alice and Bob each arrive at a party at a random time between $1:00$ and $2:00$. If Alice arrives after Bob, what is the probability that Bob arrived before $1:30$

Answer 1

The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

According to the question,

Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.

In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.

Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.

s = {(x, y) /1≤x≤2 and 1≤y≤2}

In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.

Formula for Probability = $\frac{Number of favorable events}{Total number of events}$

= 1/2

Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

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