Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 10 Counting Methods and Probability - 10.5 Find Probabilities of Independent and Dependent Events - 10.5 Exercises - Skill Practice - Page 722: 36


At least $25$ throws.

Work Step by Step

The chance of us rolling two sixes at least once is one minus the probability of us not throwing two sixes, which is $1-(\frac{35}{36})^n$ after $n$ throws. This is because each throw is independent, and out of the $36$ possibilities $35$ are not two sixes. Hence $1-(\frac{35}{36})^n\geq0.5\\(\frac{35}{36})^n\leq0.5\\n\geq\log_{\frac{35}{36}}0.5\approx24.6$ Thus we need at least $25$ throws.
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