The probability that it rains on any given day in a certain town is \(0.35\). Find the probability that it does not rain on either of two particular days.
Question 1 Report
The probability that it rains on any given day in a certain town is \(0.35\).
Find the probability that it does not rain on either of two particular days.
Answer Details
The two days are independent, so the probability of a particular pair of outcomes is the product of the separate probabilities.
First find the probability of no rain on one day. Raining and not raining are the only two possibilities, so they sum to \(1\):
\(P(\text{no rain}) = 1 - 0.35 = 0.65\).
For no rain on both days, multiply: \(0.65 \times 0.65\) [M1].
By hand, \(65 \times 65 = 4225\), and there are four decimal places in total, so the answer is \(0.4225\) oe [A1]. As a fraction this is \(\dfrac{169}{400}\).
Adding the probabilities would give \(1.3\), which is impossible since no probability can exceed \(1\). That check alone rules out addition. Note also that the answer is smaller than \(0.65\), as it must be: requiring two events together is harder than requiring one.
Download The App On Google Playstore
Everything you need to excel in your exams
