Respuesta :
If Alice and Bob both go to a party which starts at 5:00 and each of them arrives at a random time between 5:00 and 6:00, then the probability that the sum of the number of minutes Alice is late for the party and the number of minutes Bob is late for the party, being less than 45 is [tex]\frac{9}{32}[/tex].
As per question statement, Alice and Bob both went to a party which started at 5:00 and each of them arrived at a random time between 5:00 and 6:00.
We are to calculate the probability that the sum of the number of minutes Alice is late for the party and the number of minutes Bob is late for the party, being less than 45.
The graph of all the possible arrival times of both Alice and Bob, in minutes after 5 P.M., is bounded by (x = 0), (y = 0) and (x= 60), (y = 60).
Let the "x" values in the graph be the number of minutes after 5 P.M. that Alice arrives at the party and the "y" values be the number of minutes after 5 P.M. that Bob arrives at the party. For example, at (0,0), both arrive at 5 P.M. and at (60,60), both arrive at 6 P.M.
But, the times we are interested in, lies beneath the graph of
[(x + y) ≤ 45].
And this area is bounded by (x = 0), (y = 0) and [(x + y) ≤ 45], which equals to [tex]\frac{45^{2} }{2}=1012.5[/tex] sq. units.
And noting that, the area of the total possible arrival times =
[(60 x 60) = 3600 sq units], the probability that the sum of Alice's and Bob's arrival times after 5PM are less than 45 minutes is [tex]\frac{1012.5}{3600}=\frac{9}{32}[/tex].
- Probability: In mathematics, probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
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