There are many misconceptions about probability which may include the following.

Question

There are many misconceptions about probability which may include the following.

All events are equally likely

Later events may be affected by or compensate for earlier ones

When determining probability from statistical data, sample size is irrelevant

Results of games of skill are unaffected by the nature of the participants

“Lucky/Unlucky” numbers can influence random events

In random event involving selection, results are dependent on number rather than rations

If events are random then the results of a series of independent events are equally likely

The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two.

1 I have flipped and unbiased coin three times and got heads, it is more likely to get tails the next time I flip it.

2 The Rovers play Mustangs. The Rovers can win, loose, or draw, so the probability that they win is 1/3.

3 I roll two dice and ad the results. The probability of getting a total of 6 is 1/12 because there are 12 different possibilities and 6 is one of them.

4 Mr. Purple has to have a major operation. 90% of the people who have this operation make a complete recovery. There is a 90% chance that Mr. Purple will make a complete recovery if he has this operation.

5 I flip two coins. The probability of getting heads and tails is 1/3 because I can get Heads and Heads, Heads and Tails, or Tails and Tails.

6. 13 is an unlucky number so you are less likely to win raffles with ticket number 13 than with a different dumber.

Explanation / Answer

1) A coin toss is an independent event. The result of a previous coin toss cannot influence the results of subsequest coin tosses because there is no relationship between them.

2) Probabilty of each of these events is not same as these are not equi-probable event. Probability of rovers winning can be 0.2 or 0.5 or even 0.9 . All these probabilities should however sum to 1.

3) THere are 36 different possibilities in the results of two dice. A total of 6 can be got in the following 5 different ways (1,5) (2,4) (3,3) (4,2) (5,1) . Hence the probabiity is 5/36.

4) The chances for Mr. Purple to make a complete recovery 90% is dependent upon him, the operation, and the people who is performing the operation. But this still does not mean that he has the same chances as the other 90% that recovered completely from the surgery.

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