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If a certain coin is flipped, the probability that the coin

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Re: If a certain coin is flipped, the probability that the coin [#permalink] New post 03 Apr 2012, 23:39
Expert's post
dchow23 wrote:
whats the difference between this question and the following?

If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?

is it because it could any 3 days between the 4th and 8th?


The difference is explained here: if-a-certain-coin-is-flipped-the-probability-that-the-coin-58357.html#p1049993

The probability of rain each day is 1/2 and the probability of no rain is also 1/2. C^3_5=10 represent ways to choose on which 3 days out of 5 there will be a rain, so P=C^3_5*(\frac{1}{2})^3*(\frac{1}{2})^2=\frac{10}{32}=\frac{5}{16}.

Or think about it this way: we want the probability of the following event: RRRNN, where R represent rain day and N represents no-rain day. Now, each R and each N have individual probability of 1/2, so (\frac{1}{2})^5.

But the case of RRRNN can occur in many ways: RRRNN, RRNRRN, RNRRN, NRRRN, ... basically it will be equla to # of arrangements (permutations) of 5 letters RRRNN out of which there are 3 identical R's and 2 identical N's. That # of arrangements is \frac{5!}{3!2!}, (notice that it's the same as C^3_5). So, finally P=\frac{5!}{3!2!}*(\frac{1}{2})^5=\frac{5}{16}.

For more on this topic check Combinations and Probability chapters of Math Book:
math-combinatorics-87345.html
math-probability-87244.html

Also check similar questions to practice:
if-the-probability-of-rain-on-any-given-day-is-50-what-is-99577.html
on-saturday-morning-malachi-will-begin-a-camping-vacation-100297.html
what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html
there-is-a-90-chance-that-a-registered-voter-in-burghtown-56812.html
combination-ps-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html?

Hope it helps.
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Re: If a certain coin is flipped, the probability that the coin [#permalink] New post 10 Jul 2013, 08:54
My try ( I am a beginner trying to solve this kind of problems using combinations :idea:

\frac{C^5_3}{{(C^2_1)^5}} = 1/32

C^5_3 : number of combinations in which we obtain 3 H in 5 tosses

(C^2_1)^5 : number of combinations of T or H in 5 tosses
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Re: If a certain coin is flipped, the probability that the coin   [#permalink] 10 Jul 2013, 08:54
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