Question

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. $65\%$

Answer 1

The correct option is A $10\%$

Probability of rain today is $60$ percent and probability of rain tomorrow is $75$ percent. they are independent.(let $100$ percent be $1$, so we get $0.6$ and $0.75$ as probabilities).

Now the probability of intersection is $0.6\times 0.75=0.45$

Probability that rain will fall today or tomorrow is $0.6+0.75-0.45=0.9$

Therefore probability that that rain will neither fall today nor tomorrow is $1-0.9=0.1$, which implies $10$ percent.