Step-by-step explanation:





Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:

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Answer
Find out how many seconds faster has Alexandria's time then Adele's time .
To proof
Let us assume that seconds faster has Alexandria's time then Adele's time be x.
As given in the question
Adele Swam the length of the pool in 32.56 seconds. Alexandria swam the length of the pool in 29.4 seconds.
Than the equation becomes
x = 32.56 - 29.4
x = 3.16 seconds
Therefore the 3.16 seconds faster has Alexandria's time then Adele's time .
Hence proved
The answer will be 210 seconds. 60 X 3 = 180+ 30= 210