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Three Probability Problems

Elfen
over 6 years

  1. We toss a biased (an unfair) coin 10 times. The coin has a probability of tossing heads p. Calculate the probability that there are 5 heads in the first 8 tosses and 3 heads in the last 5 tosses (both of them must happen), in terms of p. [Solved by HardCarry]

  2. Suppose there is a crazy professor who grades some submissions with marks {1, 2, 3, 4, 5, 6} and he does it totally randomly. How many times is the mean value of submissions, in which you will have every mark at least once? [Solved by HardCarry]

  3. Suppose there are 2n persons who form n couples. Suppose that after many years, the probability of a person being alive is p, and it is equally likely for all persons. On condition that after many years, m people are alive, find the mean value of couples who have both persons alive. (on terms of m and n)

HardCarry
over 6 years
My solution for Question 2:

Elfen
over 6 years

HardCarry says

I'll try #2 later tonight but is it asking the mean number of submissions which will get you all 6 marks?


Yes.

For example if we roll {2,5,4,3,4,4,4,2,1,4,2,5,6} would equal to 13 submissions.
HardCarry
over 6 years
I'll try #2 later tonight but is it asking the mean number of submissions which will get you all 6 marks?
deletedover 6 years
Yes!
Elfen
over 6 years

bonk says

here's a funny one

You're watching the news and there's two weathermen on air currently. The first weatherman is 70% accurate, the second weatherman is 40% accurate. They both predict that it will rain today. What is the probability that is actually rains?


Is there a solution to this? Lol
Elfen
over 6 years

HardCarry says

OK, I made a small mistake in my last answer and forgot to divide by Pr(B): I think this should be correct??






This is totally correct
deletedover 6 years
here's a funny one

You're watching the news and there's two weathermen on air currently. The first weatherman is 70% accurate, the second weatherman is 40% accurate. They both predict that it will rain today. What is the probability that is actually rains?
marry
over 6 years
is this math? it must be math because I looked at it for 3 seconds and started to get a headache so I stopped reading it
deletedover 6 years
no why are u ppl like this
HardCarry
over 6 years
OK, I made a small mistake in my last answer and forgot to divide by Pr(B): I think this should be correct??

HardCarry
over 6 years
Dunno at all if this is right or not, but I gave Question 1 a stab.

HardCarry
over 6 years
Dunno at all if this is right or not, but I gave Question 1 a stab.

https://i.imgur.com/Rz1f9tg.png[\img]
hedger
over 6 years
When Sirp tries to sound smart but just ends up making a fool out of himself
Elfen
over 6 years
In 1 you don't need to find the p, you cannot actually, you need to write the answer with p inside.

Problem 3 doesn't care about the years. You just assume that there is a moment in the future where everyone has a probability p of being alive.
SirPerior
over 6 years
This isn't probability so much as thinking way too much outside the box, but for problem 3, based on how one infers the connotation of "many" years, it could easily 100 years, or 500 years, or many more than that. If one also assumes that these are average humans with a life expectancy of 80 years or so, then the answer is clearly 0, because they would all be dead.
deletedover 6 years
i gave up on problem 1 but P=0.613
MonteCarrlo
over 6 years
1. 100% because i rigged the data.
2. 5 because I rigged the data.
3. 40 because my wife forced me to rig the data!
EMOlympics
over 6 years
i can't even do simple math reflex let alone this