explain why simulation fails to model real situation properly 3. Explain why eac

Question

explain why simulation fails to model real situation properly 3. 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 digits from 1 through 13 to represent the denominations of the cards in a five-card poker 4 Devise and use a simulation to answer this question: Many couples want to have both a boy and a girl If they decide to continue to have children until they have one child of each sex, what would the average family size be? Assume that boys and girls are equally likely

Explanation / Answer

Let's try to find out first, for each of these 3 given conditions - which scenarios may represent a highly likely situation which may happen in reality with those given conditions?.. so that we can figure out the difference between the given simulations vs. those that can represent reality.

a)

When we toss 9 coins, assuming all of them to be real coins, close to having enough fairness for head or tail results, the probability for all of the coins to result in a head or tail is 50 - 50 %.

And so when we toss them, in reality it is highly likely to get a split of 4 or 5 (50% of 9 is 4.5) number of heads vs. tails or vice a versa respectively, as a result owing to the almost unbiased nature of real coins.

As we know from the bell curve of normal distribution, the observation representing the mean has the highest likelyhood to happen in reality, and those cases which deviates farther from the observation corresponding to the mean, have proportionally lesser probability to happen..

So owing to this inversely proportional relationship to the difference or distance from 4.5 (mean) , if we select any digits which are farther from digit representing the mean observation of 4 and 5 will have proportionally lesser likelyhood to happen in reality, in contrast to any randomly selected digits.

So the closest simulation which would represent reality for scenario 3a of tossing 9 coins would be 4 or 5 heads and not a random digit selection where all the digits would have an equal likelyhood!

b)

Similar to above explanation we can say that in reality a professional basketball player should have significantly higher likelyhood of converting a foul shot into a good hit rather than a miss, whereas if we select any even digit to represent a good hit and odd ones to a miss, we get a 50 - 50 % or equall likelyhood of hit and miss which is typically unreal for any good basketball player..

c)

In any card games like poker for example, as the shuffled cards are getting evenly distributed among players, the probability of receiving those denominations - which have already been distributed - receeds with each delivery of that particular denomination.

e.g. Let's say that at a particular point of time during cards distribution, 3 Ace cards have already been distributed however none of the Kings have been received yet by any player.

So during the rest of the distribution, Kings have 4 times higher likelyhood than that of the remaining ace to be received.

Similarly if there are 3 players of 5 card poker and if 2 of them have not received any Ace card, it is highly likely for the remaining player to have an Ace in his or her set of 5 cards than any other denomination which have already been received by those 2 opponents.

Considering this characteristic of reduction in probability of receiving any particular denomination with its delivery or selection elsewhere, if we randomly select any of the 1 to 13 denominations with equal likelyhood, it will fail to represent the real simulation which should reduce this probability along with selection of any particular denomination.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.