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Math  /  Data & Statistics

Questionpst-test Question 9, 11.3.11 HW Score: 38.75%,7.7538.75 \%, 7.75 of 20 points Points: 0 of 1 Save
At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If five fortune cookies contain " $1\$ 1 off," four contain "\3off,"andonecontains"3 off," and one contains " \7 7 off," determine the expectation of a selection. □\square dollars off (Round to the nearest cent.)

Studdy Solution
Calculate the expected value (E) using the formula: E=($1×P($1 off))+($3×P($3 off))+($7×P($7 off))E = (\$1 \times P(\$1 \text{ off})) + (\$3 \times P(\$3 \text{ off})) + (\$7 \times P(\$7 \text{ off}))
Substitute the probabilities: E=($1×0.5)+($3×0.4)+($7×0.1)E = (\$1 \times 0.5) + (\$3 \times 0.4) + (\$7 \times 0.1)
Calculate each term: E=0.5+1.2+0.7E = 0.5 + 1.2 + 0.7
Sum the terms: E=2.4E = 2.4
The expected value of a selection is:
2.40 dollars off\boxed{2.40} \text{ dollars off}

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