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:
62>32>16>8>>4>2>1
Add them all up and you get 125
So there was a total of 125 games played in the regional soccer tournament.
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If diagonals of a parallelogram are perpendicular to each other, this is a rhombus. A rhombus has all sides equal.
In the current scenario, the shorter rhombus is 20 cm long and has a perimeter of 80 cm
Side of rhombus = 80/4 = 20 cm
A quarter of rhombus is right angled triangle with hypotenuse being side of rhombus.
Half length of long diagonal = sqrt (20^2-10^2) = 17.32 cm
Length of longer rhombus = 17.32*2 = 34.64 cm
Answer:
5/6, there are 5 non V sides and only 1 V side
Step-by-step explanation:
Answer:
They can finish the race in 15 x 14 x 13 x 12 x 11 = 360360 order.
Step-by-step explanation:
There are 15 bicyclists in the race. The first position would come from the first bicyclist to the 15th. Meaning the first position can be occupied by 15 individuals. The second position can only be occupied by 14 individuals since one person is already first. Same way the third, fourth and fifth positions can be occupied by 13, 12 and 11 individuals respectively.
Therefore, they can finish the race in
15 x 14 x 13 x 12 x 11 = 360360 order.
