There's a .70 probability of rain. So each day has a .70 probability that it will rain, times itself 15 times to get 15 total days. In other words:
(.70)(.70)\text\ 15\ times\ for\ the \ 15\ days.\ Hence\ .70^{15})
That leaves a .30 probability that it won't rain. So you need 15 days that it won't rain, at a .30 probability for each one. So
(.30)(.30) \text\ 15\ times,\ hence\ (.30)^{15})
Hence, the
^{15}(.30)^{15})
Which gives us the equation:
^{n-x})
where x is how many you're looking for (15 days) and n is the total.
You're multiplying out the probability of "success" (as defined by what you're looking for, in this case, rain) the number of times you're looking for it to happen. Then multiplying out the probability of failure times the number of times it will happen.
But that's only if the first 15 days are the ones during which it rains and the last 15 the ones when it doesn't rain. So we add the combination in front of it to account for the number of ways we could combine rain with no rain, as ebaines pretty much already went over. So we have the total equation:
p^x(1-p)^{n-x})
Linear Mode
