Question

A rainy day occurs once in every 10 days. Half of the rainy days produce rainbows. What percent of all the days do not produce a rainbow?

• A. 95%
• B. 10%
• C. 50%
• D. 5%

Hint:

If event $B$ happens on a fraction of event $A$ days, then $P(B)=P(B|A) P(A)$. Here $P(B|A)=\tfrac12$ and $P(A)=\tfrac110$.

Answer 1

The Correct Option is A

Step 1: Probability of a rainy day.
“Once in every 10 days” ⇒ $P(\text{rain})=\dfrac{1}{10}=0.1$.
Step 2: Probability of a rainbow on a given day.
Half of rainy days produce rainbows ⇒ \[ P(\text{rainbow})=\tfrac{1}{2} P(\text{rain}) =\tfrac{1}{2} 0.1 = 0.05 = 5%. \] Step 3: Percent of days with no rainbow.
\[ 100% - 5% = 95%. \] \[ \boxed{95%} \]