At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
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.
To learn more about Probability, click on the link below.
https://brainly.com/question/11234923
#SPJ4
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
