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.

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

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.

This statement is incorrect because if we flip two coins, the sample space will be:

{Heads and Heads, Heads and Tails, Tails and Heads, Tails and Tails}

Hence,

Heads and tails can occur in 2 ways i.e. heads on first coin, tails on second and tails on first coin, heads on second.

Therefore,

The probability of heads and tails will be 2/4 i.e. 1/2.

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

This statement is incorrect because in raffles, all the numbers are equally likely. So the probability of winning with a ticket number 13 will be the same as probability of winning with any other ticket number.

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