# Thread: Probability Question regarding tossing of a coin

1. ## Probability Question regarding tossing of a coin

Question :

How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?

2. Originally Posted by zorro
Question :

How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?
Find the number of tosses such that Pr(no heads) = 0.125.

Note that if X is the random variable 'number of heads' then X ~ Binomial(n = ?, p = 1/2) and Pr(X = 0) = 0.125. Substitute into the usual formula and solve for n.

3. ## How did u get that

Originally Posted by mr fantastic
Find the number of tosses such that Pr(no heads) = 0.125.

Note that if X is the random variable 'number of heads' then X ~ Binomial(n = ?, p = 1/2) and Pr(X = 0) = 0.125. Substitute into the usual formula and solve for n.

How did u get Pr(no heads) = 0.125.

4. Originally Posted by zorro
How did u get Pr(no heads) = 0.125.

Originally Posted by zorro
[snip]probability of getting atleast one head is 0.875

You need to review the basic rules relating to complementary events.

5. ## I am still having problem

Originally Posted by mr fantastic

You need to review the basic rules relating to complementary events.
Mr fantastic i still dont know how should i find 'n'

using Binomial

$\displaystyle p(x,n,\theta)$ = $\displaystyle \binom{n}{x} \theta^x (1- \theta)^{n-x}$

$\displaystyle p(0,n,0.5)$ = $\displaystyle \binom{n}{0} (0.125)^0 (0.875)^{n}$............Is this what u meant by substituting in the usual Binomial formula

6. Originally Posted by zorro
Question : How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?
Can you solve $\displaystyle 1-(0.5)^n\ge 0.875$ for n?
That is the essence of this question.

7. ## One more problem

Originally Posted by Plato
Can you solve $\displaystyle 1-(0.5)^n\ge 0.875$ for n?
That is the essence of this question.

$\displaystyle 1 - (0.5)^n \ = \ 0.875$

$\displaystyle 0.5^n \ = \ 1 - 0.875$

$\displaystyle 0.5^n \ = \ 0.125$

$\displaystyle 0.5 \ = \ (0.125)^{1/n}$..........I am stuck here

8. Originally Posted by zorro and edited (replaced equality with inequality signs) by Mr F
$\displaystyle 1 - (0.5)^n \geq \ 0.875$

$\displaystyle 0.5^n \leq 1 - 0.875$

$\displaystyle 0.5^n \leq 0.125$

[snip]
Find (I suggest by trial and error) the minimum integer value of n that satisfies this inequality.

9. ## Thank u Mr fantastic

Originally Posted by mr fantastic
Find (I suggest by trial and error) the minimum integer value of n that satisfies this inequality.

n = 3

Thank you mr fantastic for helping me
cheers

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### how many tosses of a coin are needed so that the probability of getting at least one head is 0.875?

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