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QuestionIf there is a 0.8%0.8 \% chance that none of the books you would like to check out of the library are available, what is the probability that at least one of the books you want is available? Round to 1 decimal place as needed. Be sure to convert to \% and include your \% in the answer.
Your Answer: □\square Answer □\square units

Studdy Solution

STEP 1

1. The probability that none of the books are available is given as 0.8%0.8\%.
2. We need to find the probability that at least one book is available.

STEP 2

1. Convert the given percentage to a decimal.
2. Use the complement rule to find the probability that at least one book is available.
3. Convert the result back to a percentage and round to one decimal place.

STEP 3

Convert the given percentage to a decimal:
P(None available)=0.8%=0.8100=0.008 P(\text{None available}) = 0.8\% = \frac{0.8}{100} = 0.008

STEP 4

Use the complement rule to find the probability that at least one book is available:
P(At least one available)=1−P(None available) P(\text{At least one available}) = 1 - P(\text{None available}) =1−0.008 = 1 - 0.008

STEP 5

Calculate the probability:
P(At least one available)=1−0.008=0.992 P(\text{At least one available}) = 1 - 0.008 = 0.992
Convert the result back to a percentage:
P(At least one available)=0.992×100%=99.2% P(\text{At least one available}) = 0.992 \times 100\% = 99.2\%
Round to one decimal place:
99.2% \boxed{99.2\%}

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