Respuesta :
Answer:
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
