The probability that it will rain on particular day of week is 50%. Find the probability that it rains only on the first 4 days of the week.
My approach :
Probability of raining on any particular day is 50% = p = $\frac{1}{2}$ , probability of not raining on particular is also 50% = q = $\frac{1}{2}$
Probability that it rains only on the first 4 days of the week = $^nC_r(p)^r(q)^{n-r} $ [ using binomial distribution]
here n = 7 , r = 4
therefore, the required probability = $^7C_4(p)^4(q)^{7-4} $ = $^7C_4(\frac{1}{2})^4(\frac{1}{2})^3$
Can you please suggest whether it is the right answer.. thanks in advance….
Best Answer
The answer is actually $\left( \frac{1}{2} \right)^4 \left(1 - \frac{1}{2} \right)^3 = \frac{1}{128}$, as there is only one permutation of days which satisfies this, not $7 \choose 4$.
What you have written answers a different question. The formula for binomial probability should be used when it does not matter which days are chosen. It would be correct only if the question were: "Find the probability it rains exactly $4$ times during the week".