Question

The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two. 1.The number 7 is a lucky number so you are more likely to win raffles with ticket number 7 than with a different number. 2.I roll two dice and add the results. The probability of getting a total of 8 is 1/12 because there are 12 different possibilities and 8 is one of them. 3.Mr. Verde has to have a major operation. Ninety-three percent of the people who have this operation make a complete recovery. There is a 93% chance that Mr. Verde will make a complete recovery if he has this operation.4.The Ramblers play the Chargers. The Ramblers can win, loose, or draw, so the probability that they win is 1/3. 5.I have flipped an unbiased coin four times and got heads. It is more likely to get tails the next time I flip it.6.Thirty random college students are asked if they study during the week. Since 60% said yes, a statement can be made that 40% of students only study on the weekend.

Answer 1

The reasons for each incorrect statement are as follows;

1. The error in the statement is that, there might be other luckier numbers compared to number 7 and hence, the statement does not hold true for all numbers.
2. The statement is incorrect because, there are 36 different possibilities and there are 5 possibilities of getting an 8.
3. The statement is incorrect because, 93% does not necessarily represent a 93% chance of complete recovery as this is subject to other variables.
4. The probability that they win is not 1/3 as it is subject to what the results have been over the years and not just the possible results.
5. Since, the coin is unbiased, it follows that upon flipping the coin for the fifth time, it is not likely to have tails the next time it is flipped.
6. The statement is incorrect because some students study during the week and weekends, hence, the conclusion is not correct.

What is Probability?

The term probability put simply is the ratio of the desired outcome to the possible outcomes. It therefore follows that probability as the name implies is used to predict the chance of an occurrence.

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Answer 2

The probability is illustrated below.

How to illustrate the probability?

1) Raffles game is a gambling competition in which people get numbered tickets and each number has an equal chance of winning.

2) When two dice are rolled then there will be totally 36 outcomes. Of those the outcomes with sum 8 are (2,6),(3,5),(4,4),(5,3),(6,2).

These are 5 in number.

So,P( sum =8)= 5/36.

3)This is a true statement.

4) Here win, lose, or tie is just the outcomes where their probabilities are different from each other and those values depend upon different situations.

5) Tossing a coin is a random experiment which means that the result of the experiment (ie head or tail) cannot be predicted.

6) If 60% said yes to " study during the week" then 40% will say yes to "either won't study or study at weekend".

7) When two coins are tossed, the outcomes are as follows

H,H

H,T

T,H

T,T.

So, P( head, tail ) =2/4 =1/2

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