There is a 40% chance it will rain today, a 25% chance it will snow today, and a 15% chance that it will rain and snow. Are the two events "rain today" and "snow today" independent events? Explain your answer.

Let's recall that two events are independent if the result of the 2nd event is not affected by the result of the 1st event. If "rain today" and "snow today" are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

P (R and S) = P (R) * P (S)

P (R and S) = 0.4 * 0.25 = 0.1

The information given is that P (R and S) = 0.15 and 0.15 ≠ 0.1, therefore the two events: "rain today" and "snow today", for this question, are not independent events.

Step-by-step explanation:

1. Let's check the information given to answer the question:

P (R) : probability of rain today (A = 40% = 0.4);

P (S) : probability of snow today (B = 25% = 0.25)

P (R and S) = probability of rain today and snow today (R and S = 15% = 0.15)

2. Are the two events "rain today" and "snow today" independent events? Explain your answer.

Let's recall that two events are independent if the result of the 2nd event is not affected by the result of the 1st event. If "rain today" and "snow today" are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

P (R and S) = P (R) * P (S)

P (R and S) = 0.4 * 0.25 = 0.1

The information given is that P (R and S) = 0.15 and 0.15 ≠ 0.1, therefore the two events: "rain today" and "snow today", for this question, are not independent events.