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**Hannibal lecter****Member**- Registered: 2016-02-11
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a fair coin is tossed 40 times, find the probability of getting 10 Heads!

can anyone solve this please

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 100

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.

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**Hannibal lecter****Member**- Registered: 2016-02-11
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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?

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,173

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!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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