The probability of rain today is 60 percent, and the independent probability of rain tomorrow is 75 percent. Calculate the probability that it will rain neither today nor tomorrow.

• (a). 10%
• (b). 15%
• (c). 45%
• (d). 55%
• (e). 65%

To find the probability that it will not rain today or tomorrow, we first need to determine the probabilities of it not raining on each day.

Step 1: Calculate the Probability of No Rain

The probability of no rain today is:

• Probability of rain today = 60% = 0.60
• Probability of no rain today = 1 - 0.60 = 0.40 (or 40%)

For tomorrow, the probability of no rain is:

• Probability of rain tomorrow = 75% = 0.75
• Probability of no rain tomorrow = 1 - 0.75 = 0.25 (or 25%)

Step 2: Calculate the Combined Probability

Since the probabilities are independent, we multiply the probabilities of no rain on both days:

• Probability of no rain today and tomorrow = 0.40 * 0.25 = 0.10 (or 10%)

Final Answer

The probability that it will rain neither today nor tomorrow is 10%. Therefore, the correct option is (a).