Question

1. a grab-bag contains 20 packages worth $.70 each, 15 packages $.60 cents each, and 5 packages worth $.30 each. what is the expected value if you have to pay $.50 to pick one package at random?

about $0.60
about $0.11
about $0.00
about $0.53

Explanation:

Step1: Calculate total packages

Total packages = 20 + 15 + 5 = 40.

Step2: Find probabilities

Probability of $0.70 package: $P_1 = \frac{20}{40} = 0.5$.
Probability of $0.60 package: $P_2 = \frac{15}{40} = 0.375$.
Probability of $0.30 package: $P_3 = \frac{5}{40} = 0.125$.

Step3: Calculate expected value of package

Expected value (package) = $(0.70 \times 0.5) + (0.60 \times 0.375) + (0.30 \times 0.125)$
= $0.35 + 0.225 + 0.0375 = 0.6125$.

Step4: Subtract cost to pick

Expected value = $0.6125 - 0.50 = 0.1125 \approx 0.11$.

Answer:

about $0.11