Suppose the probability that it rains on a given day is $0.3$. What is the probability that it does not rain on that day?

• A. $0.5$
• B. $0.7$
• C. $0.3$
• D. $1.0$

Answer: (B)

Verified step by step guidance

1. Understand that the problem involves the probability of complementary events: rain and no rain on a given day.
2. Recall that the sum of probabilities of all possible outcomes must equal 1. In this case, the two outcomes are 'rain' and 'no rain'.
3. Let \(P(\text{rain})\) be the probability that it rains on a given day, which is given as 0.3.
4. The probability that it does not rain, \(P(\text{no rain})\), is the complement of \(P(\text{rain})\). Use the formula for complementary events: \(P(\text{no rain}) = 1 - P(\text{rain})\)
5. Substitute the given value into the formula: \(P(\text{no rain}) = 1 - 0.3\) This will give you the probability that it does not rain on that day.