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Q. 14

Expert-verified
Found in: Page 865

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

In Problems 11–16, construct a probability model for each experiment.Tossing a fair coin, a fair die, and then a fair coin.

The list of possible outcomes:

$S=\left\{\mathrm{H}1\mathrm{H},\mathrm{H}2\mathrm{H},\mathrm{H}3\mathrm{H},\mathrm{H}4\mathrm{H},\mathrm{H}5\mathrm{H},\mathrm{H}6\mathrm{H},\mathrm{H}1\mathrm{T},\mathrm{H}2\mathrm{T},\mathrm{H}3\mathrm{T},\mathrm{H}4\mathrm{T},\mathrm{H}5\mathrm{T},\mathrm{H}6\mathrm{T},\mathrm{T}1\mathrm{H},\mathrm{T}2\mathrm{H},\mathrm{T}3\mathrm{H},\mathrm{T}4\mathrm{H},\mathrm{T}5\mathrm{H},\mathrm{T}6\mathrm{H},\mathrm{T}1\mathrm{T},\mathrm{T}2\mathrm{T},\mathrm{T}3\mathrm{T},\mathrm{T}4\mathrm{T},\mathrm{T}5\mathrm{T},\mathrm{T}6\mathrm{T}\right\}$

The probability of each outcome will be $\frac{1}{24}$.

See the step by step solution

Step 1. Given information.

Construct a probability model for experiment: Tossing a fair coin, a fair die, and then a fair coin.

Step 2. Construct probability model.

Considering the following outcomes for a coins, a die and another coin:

First coin - A head (H) or a tail (T), A die - 1,2,3,4,5 and 6 and Second coin - A head (H) or A tail (T).

$S=\left\{\mathrm{H}1\mathrm{H},\mathrm{H}2\mathrm{H},\mathrm{H}3\mathrm{H},\mathrm{H}4\mathrm{H},\mathrm{H}5\mathrm{H},\mathrm{H}6\mathrm{H},\mathrm{H}1\mathrm{T},\mathrm{H}2\mathrm{T},\mathrm{H}3\mathrm{T},\mathrm{H}4\mathrm{T},\mathrm{H}5\mathrm{T},\mathrm{H}6\mathrm{T},\mathrm{T}1\mathrm{H},\mathrm{T}2\mathrm{H},\mathrm{T}3\mathrm{H},\mathrm{T}4\mathrm{H},\mathrm{T}5\mathrm{H},\mathrm{T}6\mathrm{H},\mathrm{T}1\mathrm{T},\mathrm{T}2\mathrm{T},\mathrm{T}3\mathrm{T},\mathrm{T}4\mathrm{T},\mathrm{T}5\mathrm{T},\mathrm{T}6\mathrm{T}\right\}$

The probability of each outcome will be $\frac{1}{24}$ since each of them appeared once in the sample space with 24 total outcomes. If we will add them together, it will be equal to 1.

Step 3. Conclusion.

The list of possible outcomes:

$S=\left\{\mathrm{H}1\mathrm{H},\mathrm{H}2\mathrm{H},\mathrm{H}3\mathrm{H},\mathrm{H}4\mathrm{H},\mathrm{H}5\mathrm{H},\mathrm{H}6\mathrm{H},\mathrm{H}1\mathrm{T},\mathrm{H}2\mathrm{T},\mathrm{H}3\mathrm{T},\mathrm{H}4\mathrm{T},\mathrm{H}5\mathrm{T},\mathrm{H}6\mathrm{T},\mathrm{T}1\mathrm{H},\mathrm{T}2\mathrm{H},\mathrm{T}3\mathrm{H},\mathrm{T}4\mathrm{H},\mathrm{T}5\mathrm{H},\mathrm{T}6\mathrm{H},\mathrm{T}1\mathrm{T},\mathrm{T}2\mathrm{T},\mathrm{T}3\mathrm{T},\mathrm{T}4\mathrm{T},\mathrm{T}5\mathrm{T},\mathrm{T}6\mathrm{T}\right\}$

The probability of each outcome will be $\frac{1}{24}$.