The probability of rain on any given day in NJ is 0.33. Today is January 15. What is the probability that you have to wait less than seven more days before you it rains

0.9095

Step-by-step explanation:

Probability of rain any given day = 0.33.

Probability of no rain = 0.67

We require probability that it rains before the next 7 days pass by. P (X < 7)

This is a sum of probabilities that involve probability of first rain, the next day, up until the 6th day.

For rain to come the next day

Probability = 0.33

Rain coming On the 2nd day since Jan 15, that is, no rain on the first day, rain on the 2nd day

Probability = 0.67 * 0.33 = 0.2211

Wait till the 3rd day before rain

Probability = 0.67 * 0.67 * 0.33 = 0.148137

Wait till the 4th day before rain

Probability = 0.67 * 0.67 * 0.67 * 0.33 = 0.09925179

Wait till the 5th day before rain

Probability = 0.67 * 0.67 * 0.67 * 0.67 * 0.33 = 0.0664986993

Wait till the 6th day before rain

Probability = 0.67 * 0.67 * 0.67 * 0.67 * 0.67 * 0.33 = 0.0445541285

probability that it rains before the next 7 days pass by = 0.33 + 0.2211 + 0.148137 + 0.09925179 + 0.0664986993 + 0.0445541285 = 0.9095