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Adriana and her best friend wanted to paint their apartment. In their storage closet, they found 99 cans of paint. Adriana remembered that 77 of the cans contained light blue paint, but none of the cans had labels.\newlineIf Adriana randomly opened 66 cans, what is the probability that all of them contain light blue paint?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____\newline

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Q. Adriana and her best friend wanted to paint their apartment. In their storage closet, they found 99 cans of paint. Adriana remembered that 77 of the cans contained light blue paint, but none of the cans had labels.\newlineIf Adriana randomly opened 66 cans, what is the probability that all of them contain light blue paint?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____\newline
  1. Calculate probability of first can: Calculate the probability of the first can being light blue. Since there are 77 light blue cans out of 99 total cans, the probability is 79\frac{7}{9}.
  2. Calculate probability of second can: Calculate the probability of the second can being light blue after one light blue can is already taken out.\newlineNow there are 66 light blue cans left and 88 cans in total, so the probability is 68\frac{6}{8}.
  3. Calculate probability of third can: Calculate the probability of the third can being light blue. Now there are 55 light blue cans left and 77 cans in total, so the probability is 57\frac{5}{7}.
  4. Calculate probability of fourth can: Calculate the probability of the fourth can being light blue. Now there are 44 light blue cans left and 66 cans in total, so the probability is 46.\frac{4}{6}.
  5. Calculate probability of fifth can: Calculate the probability of the fifth can being light blue. Now there are 33 light blue cans left and 55 cans in total, so the probability is 35\frac{3}{5}.
  6. Calculate probability of sixth can: Calculate the probability of the sixth can being light blue. Now there are 22 light blue cans left and 44 cans in total, so the probability is 24\frac{2}{4}.
  7. Multiply all probabilities: Multiply all the probabilities together to get the overall probability.\newline(79)×(68)×(57)×(46)×(35)×(24)=79×34×1×23×35×12(\frac{7}{9}) \times (\frac{6}{8}) \times (\frac{5}{7}) \times (\frac{4}{6}) \times (\frac{3}{5}) \times (\frac{2}{4}) = \frac{7}{9} \times \frac{3}{4} \times 1 \times \frac{2}{3} \times \frac{3}{5} \times \frac{1}{2}
  8. Simplify multiplication of fractions: Simplify the multiplication of the fractions. \newline79×34×23×35×12=7×3×2×3×19×4×3×5×2\frac{7}{9} \times \frac{3}{4} \times \frac{2}{3} \times \frac{3}{5} \times \frac{1}{2} = \frac{7 \times 3 \times 2 \times 3 \times 1}{9 \times 4 \times 3 \times 5 \times 2}\newline=7×1×1×13×2×5×2= \frac{7 \times 1 \times 1 \times 1}{3 \times 2 \times 5 \times 2}\newline=760= \frac{7}{60}
  9. Convert fraction to decimal: Convert the fraction to a decimal and round to four decimal places. \newline760=0.1167\frac{7}{60} = 0.1167

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