Question

On any day, the probability of rain is 0.3. The occurrence of rain on any day is independent of the occurrence of rain on any other day. Calculate the probability that, starting with tomorrow, the second day ofrain will occur within 5 days.

Answer 1

Answer: 0.47178  Step-by-step explanation: Find the probability for each p(X=x) up to 5 using the equation: (x-1)C(r-1)*p^r * q^x-r, where x is number of days, p = .3 (prob of rain). q=.7 (prob of not rain), and r=2 (second day of rain). also C means choose. So p(X=1) = 0 p(X=2) = 1C1 * .3^2 * .7^0 = .09 P(X=3) = 2C1 * .3^2 * .7^1 = .126 P(X=4) = 3C1 * .3^2 * .7^2 = .1323 P(X=5) = 4C1 * .3^2 * .7^3 = .12348 Then add all of them up 0+.09+.126+.1323+.12348 = .47178