5.50 Independent or dependent trial and probability: Gamblers often falsely pred

Question

5.50 Independent or dependent trial and probability: Gamblers often falsely predict the outcomes of a future trial based on the outcome of previous trials. When trials are independent the outcome of a future trial cannot be predicted based on the outcomes of previous trails. For each of the following examples, (1) state whether the trials are independent or dependent and (2) explain why. In addition, (3) state whether it is possible that the quote is accurate or whether it is definitely fallacious, explaining how the independence or dependence of trials influence accuracy.

a, You are playing Monoply and have rolled a pair of sixes in 4 out of your 10 rolls of the dice. You say, "Cool, I'm on a roll and will get sixes again."

b. You are Ohio State University football fan and are sad because the team has lost two games in a row. You say, "That is really unusual the Buckeyes are doomed this season. That's what happens with lots of early-season injuries."

c.You have a 20 yr old car that has troubles starting from time to time. It has started every day this week, and now it's Friday. You say "I'm doomed it's been reilable all week and even though I did get a tune-up last week, today is bound to be the day iy fails me."

d. It's the first week of your corporate intership and you have to wear nylon stockings to the office if you're wearing a skirt. On the first and second days, you get a run in your stockings almost immediatly, an indication of a defect. The third day, you put on yet another new pair of stockings and say "OK, this pair has to be good. There's no way I'd have three bad pairs in a row. They're even frm different stores!"

Explanation / Answer

a)1)The trials are independent. 2 )Because getting six on the fifth roll of the dice doesn't depend on the previous event 3)The quote may be accurate because getting six continuously for the fifth time is completely independent of the previous 4 events of getting 6.Independent trial doesn't affect accuracy.

b)1)The trials are independent. 2)Because the result of the next game doesn't depend on the result of previous two games. 3)The Quote may be correct because the early-session injuries may be the reason for losing games.independent trial doesn't affect accuracy.

c)1)The trial is dependent 2)Because the trouble in starting of the car was due to the previous faults and even after getting tune-up it troubles in starting.3)The Quote may be fallacious because he did tune-up last week and the trouble in starting has started everyday this week.A dependent trial may increase or decrease accuracy.

d)1)The trial is dependent2)Because you have to wear nylon stockings only if you are wearing a skirt i.e the event of wearing nylon stockings depends on the event of wearing skirt 3)The Quote may be fallacious because buying stockings from different stores can't guarantee a good pair.A dependent trial may increase or decrease accuracy..

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