mjjking wrote:In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

4/7
3/7
35/128
4/28
28/135

7C4 *(1/2)^4*(1/2)^3 = 35/128

C

mjjking wrote:In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

4/7
3/7
35/128
4/28
28/135

Any question which involves a 50/50 probability is really a coin flip question in disguise. The question could have been written as:

"If you flip a fair coin 7 times, what's the chance of getting exactly 4 heads?"

For coin flip questions, we can use the following formula:

Prob of getting k results out of n flips = nCk/2^n

Here, n = 7 and k = 4, so:

7C4/2^7

(7!/4!3!)/128

(7*6*5/3*2)/128

35/128

* * *

As an aside, if we understand coin flip questions we can get the right answer with 100% certainty in under 5 seconds.

With a 50/50 probability, the denominator will ALWAYS be a power of 2, i.e. 2, 4, 8, 16, 32, ....

In this particular question, only choice (c) has a denominator that's a power of 2, therefore it MUST be the correct answer to the question.

Stuart Kovinsky wrote:

mjjking wrote:In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

4/7
3/7
35/128
4/28
28/135

Any question which involves a 50/50 probability is really a coin flip question in disguise. The question could have been written as:

"If you flip a fair coin 7 times, what's the chance of getting exactly 4 heads?"

For coin flip questions, we can use the following formula:

Prob of getting k results out of n flips = nCk/2^n

Here, n = 7 and k = 4, so:

7C4/2^7

(7!/4!3!)/128

(7*6*5/3*2)/128

35/128

* * *

As an aside, if we understand coin flip questions we can get the right answer with 100% certainty in under 5 seconds.

With a 50/50 probability, the denominator will ALWAYS be a power of 2, i.e. 2, 4, 8, 16, 32, ....

In this particular question, only choice (c) has a denominator that's a power of 2, therefore it MUST be the correct answer to the question.

Thanks for the formula and trick, I find this to be very useful. The only way your statement about being a power of two is incorrect is if the answers are reduced and you don't see it. In this case, no reduction could be done.