Question

eydis is taking a trip to the beach, where the weather will either be sunny or rainy. the forecast says that theres a 20% chance of rain each day for the 5 days shes there. it rains on the first day shes there. what is the probability that the second day will be sunny instead of rainy? a 20% b 50% c 80% d 100%

Explanation:

Step1: Define total probability of weather conditions

The weather is either sunny or rainy. The sum of probabilities of all possible outcomes is 100% or 1.

Step2: Determine probability of sunny day

Given the chance of rain each day is 20%. Let \(P(\text{rain})\) be the probability of rain and \(P(\text{sunny})\) be the probability of a sunny - day. Since \(P(\text{rain})+P(\text{sunny}) = 1\), and \(P(\text{rain})=0.2\), then \(P(\text{sunny})=1 - P(\text{rain})\).

$$P(\text{sunny})=1 - 0.2=0.8 = 80\%$$

Answer:

C. 80%