Question

A box contains 14 nickels, 17 dimes and 20 pennies. if a coin is picked at random from the box, what is the average value of the draw in dollars?

Answer 1

The expected value is
.. (14*.05 +17*.10 +20*.01)/(14 +17 +20)
.. = (.70 +1.70 +.20)/51
.. = 2.60/51
.. ≈ 0.05098 . . . . dollars

Answer 2

The average value of the draw in dollars is 0.05098 dollars

Explanation:

Odds are a numerical expression. It usually expressed as a pair of numbers, used in both gambling and statistics.

P(E) is the probability of an even E occurring, then

The odds in favor of E occurring are  $\frac{P(E)}{P(E^c)}$

Whereas the odds against E occurring are  $\frac{P(E^c)}{P(E)}$. The odds are expressed as ratios of whole numbers.

Probability of an Event (Given the Odds): If the odds in favor of an event E occurring are a to b, then the probability of E occurring is

$P(E) = \frac{a}{a+b}$

The expected value is  

$=\frac{14 nickels*0.05 +17 dimes*0.10 +20 pennies *0.01}{14 +17 +20} = \frac{0.70 +1.70 +0.20}{51}=0.05098 dollars$

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