Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

fair coin probablity

a fair coin is tossed 40 times, find the probability of getting 10 Heads!

can anyone solve this please

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Wisdom is a tree which grows in the heart and fruits on the tongue

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: fair coin probablity

It can be shown that this probability problem follows the binomial distribution which is given by:

where P, p, N, n are the probability of the n successes out of a total of N for an event of probability p. Therefore, since p=0.5 (because the coin is fair), N=40 and n=10 we have:

Note: If you would like the proof that this type of discrete probability problem does, in fact, follow the binomial distribution, I can provide it to you.

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: fair coin probablity

thank you, that's amazing
but  I have another question please,

Q) two dice are thrown  if their  sum is less than 8 , what is the probability that one of them is 4?

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Wisdom is a tree which grows in the heart and fruits on the tongue

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,855

Re: fair coin probablity

Hi Hannibal lecter,

Two dice are thrown. The probability of sum less than 8 are
1,1; 1,2; 2,1; 2,2; 3,1; 1,3; 3,2; 2,3; 3,3; 4,1; 1,4; 4,2; 2,4; 4,3; 3,4.
Sample space : 15

Probability of being one of them is 4 : 1,3; 3,1; 2,2.

Probability of the given event : 3/15 = 1/5.

It hope it helps!

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