Mathematics, 06.10.2019 13:40 hailscooper7363

365 days in a year.

1) what is the probability that ten students in a class have different birthdays?
2) what is the probability that at least ten students in a class share their birthday?

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Answer from: 20068088

1) What is the probability that ten students in a class have different birthdays?
We know in one year we have 365 days (omitting leap years)

The first students can have his birthday on any day so:

P(1st student)= 365/365 = 1 (assertion)
P(2nd students) = 364/365
P(3rd students) = 363/365
P(4th students) = 362/365
P(5th students) = 361/365
P(6th students) = 360/365
P(7th students) = 359/365
P(8th students) = 358/365
P(9th students) = 357/365
P(10th students) = 356/365
Then the probability that none of the birthdays happen at the same times:
365/365 x 364/365 x 363/3654 ...357/365 x 356/365 = 0.883 or 88.3%
However there is a formula you can apply if you studied permutation
365P10/365^10 you will get the same probability 0.883 or 88.3%

2) What is the probability that at least ten students in a class share their birthday?
The negation (or COMPLEMENT in term of probability) of "at least 10" is none of the 10
In short the complement of NON E have same date is the complement of AT LEAST 10 have the same date.
We know that P(A) + P(complement of A) =1
P(NOT same date) + P(same date ) =1
0.883 + P(same date ) =1
& P(at leas...) =0.117 or 11.7%

Answer from: Quest

I'll say voice is the strongest because it give you your personal opinion on things,and your voicing your reasoning..hope that ,if not let me know what i can do :

Answer from: Quest

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

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365 days in a year.

1) what is the probability that ten students in a class have differe...