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The probability is 0.6 that an “unfair” coin will turn up

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The probability is 0.6 that an “unfair” coin will turn up  [#permalink]

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New post Updated on: 11 Mar 2012, 14:07
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A
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E

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The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least one of the tosses will turn up tails?

A. 0.064
B. 0.36
C. 0.64
D. 0.784
E. 0.936

Where's my error:
P(1)+P(2)+P(3)
6/10.4/10.4/10 + 6/10.6/10.4/10 +6/10.6/10.6/10
=0.516
:(

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Originally posted by tejal777 on 02 Nov 2009, 05:51.
Last edited by Bunuel on 11 Mar 2012, 14:07, edited 1 time in total.
Edited the question and added the answer choices with OA
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Re: “unfair” coin  [#permalink]

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New post 11 Mar 2012, 14:05
3
3
tejal777 wrote:
The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least one of the tosses will turn up tails?



Where's my error:
P(1)+P(2)+P(3)
6/10.4/10.4/10 + 6/10.6/10.4/10 +6/10.6/10.6/10
=0.516
:(


The problem with your solution is that 1 or 2 tails can occur in several ways:

THH can occur in 3 ways: THH, HTH and HHT (basically it's # of arrangements of 3 letters THH out of whihc 2 H's are identical, which is 3!/2!=3). So, you should have P(THH)=0.6*0.4^2*3!/2!;
Similarly TTH can also occur in 3 way: TTH, THT and HTT. So, you should have P(TTH)=0.6^2*0.4*3!/2!.
Notice that we don't have the same issue with TTT, since it can occur only in one way: TTT.

\(P(T\geq{1})=0.6*0.4^2*\frac{3!}{2!}+0.6^2*0.4*\frac{3!}{2!}+0.6^3=0.936\).

Answer: E.

Though this question can be solved with an easier approach: \(P(T\geq{1})=1-P(H=3)=1-0.4^3=0.936\) (the probability of at least one tails is 1 minus the probability of zero tails).

Answer: E.

Hope it's clear.
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Re: “unfair” coin  [#permalink]

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New post 02 Nov 2009, 06:09
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solve it this way:

probability that at least one of the tosses will turn up tails = 1 - probability that all will be heads

= 1 - (0.4*0.4*0.4)

= 1 - 0.064

= 0.936


where you went wrong:

probability that 1 is tails = (.6*.4*.4)+(.4*.6*.4)+(.4*.4*.6)

similarly for probability that 2 is tails.. consider all the cases..

in your solution, you have considered only one case each for both of the above..

even if you had solved it correctly, this method is longer and more complicated.. solve it as shown in my post above.. easier and quicker..

hope this helps!

cheers!
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Re: “unfair” coin  [#permalink]

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New post Updated on: 02 Nov 2009, 06:17
I'm getting. Someone correct me if i'm wrong

First time:
probability of getting tails is .6 = .6

2nd time:
probability of getting heads is (.4)(.6) = .24

3rd time:
probability of getting tails is (.4)(.4)(.6) = .144

Probability of flipping unfair coin and getting tails is .984

Originally posted by lagomez on 02 Nov 2009, 06:05.
Last edited by lagomez on 02 Nov 2009, 06:17, edited 2 times in total.
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Re: “unfair” coin  [#permalink]

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New post 11 Mar 2012, 13:46
required probability = 1 - p(3 heads)

\(= 1 - (\frac{2}{5})^3 = \frac{117}{125}\)
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Re: The probability is 0.6 that an “unfair” coin will turn up  [#permalink]

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New post 08 Dec 2014, 08:07
Wy we do not multiply 0.4^3by 3!/2! ?
So as a result we will have = 1- 0.4^3*3!/2!=0.808
I do understand that this is incorrect answer, but could not explain to myself what is wrong with it.
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Re: The probability is 0.6 that an “unfair” coin will turn up  [#permalink]

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New post 08 Dec 2014, 08:16
1
Van4ez wrote:
Wy we do not multiply 0.4^3by 3!/2! ?
So as a result we will have = 1- 0.4^3*3!/2!=0.808
I do understand that this is incorrect answer, but could not explain to myself what is wrong with it.


Factorial correction (multiplying by x!/(y!...)) account for different ways an event can occur. For example, THH can occur in 3 ways: THH, HTH and HHT, so we are multiplying by 3!/2! = 3 (3!/2! is the number of permutations of 3 letters THH where 2 T's are the same).

TTT case can occur only in one way Tails, Tails, Tails, so there is no need for factorial correction for this case.

Hope it's clear.

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Re: The probability is 0.6 that an “unfair” coin will turn up  [#permalink]

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