Question

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

• A. 95%
• B. 10%
• C. 50%
• D. 5%

Hint:

Multiply the chance of rain by the chance a rainy day gives a rainbow, then subtract that result from 100%.

Answer 1

The Correct Option is A

Step 1: Find the probability of rain.
A rainy day occurs once in every 10 days, so the chance that any given day is rainy is
\[ P(\text{rain}) = \frac{1}{10} \]

Step 2: Find the probability of a rainbow.
Only half of the rainy days produce a rainbow, so the chance of a rainbow on a given day is half of the chance of rain:
\[ P(\text{rainbow}) = \frac{1}{2} \times \frac{1}{10} = \frac{1}{20} \]

Step 3: Convert to a percentage.
\[ P(\text{rainbow}) = \frac{1}{20} = 0.05 = 5\% \]

Step 4: Find the probability of no rainbow.
"No rainbow" is the exact opposite of "rainbow", so its probability is what remains out of 100%:
\[ P(\text{no rainbow}) = 100\% - 5\% = 95\% \]

Final Answer:
95% of all days do not produce a rainbow.
\[ \boxed{95\%} \]