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Problem 11

Explain why each of the following simulations fails to model the real situation properly:
a) Use a random integer from 0 through 9 to represent the number of heads when 9 coins are tossed.
b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to represent a good shot and an even digit to represent a miss.
c) Use random numbers from 1 through 13 to represent the denominations of the cards in a five-card poker hand.

a)
The outcomes are not equally likely; for example, tossing 5 heads does not have the same
probability as tossing 0 or 9 heads, but the simulation assumes they are equally likely.
b)
The even-odd assignment assumes that the player is equally likely to score or miss the shot. In
reality, the likelihood of making the shot depends on the player's skill.
c)
Suppose a hand has 4 aces. This might be represented by $1,1,1,1$ and any other number. The
likelihood for the first ace in the hand is not the same as for the second or third or fourth. But with
this simulation, the likelihood is the same for each.

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