Question

1. the forecast predicts a 40% chance of rain on tuesday and a 60% chance on wednesday. if these probabilities are independent, what is the chance that it will rain on both days?

Explanation:

Step1: Recall the formula for independent events

For two independent events \( A \) and \( B \), the probability of both occurring is \( P(A \cap B)=P(A)\times P(B) \). Let \( A \) be the event of rain on Tuesday and \( B \) be the event of rain on Wednesday.

Step2: Convert percentages to decimals

The probability of rain on Tuesday \( P(A) = 40\%=0.4 \), and the probability of rain on Wednesday \( P(B)=60\% = 0.6 \).

Step3: Calculate the probability of rain on both days

Using the formula for independent events, \( P(A\cap B)=P(A)\times P(B)=0.4\times0.6 = 0.24 \). To convert this back to a percentage, we multiply by 100, so \( 0.24\times100 = 24\% \).

Answer:

The chance that it will rain on both days is \( 24\% \) (or \( 0.24 \) in decimal form).