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.
Flipping an unbiased coin severally presents an equal and likely chance of getting either heads or tails. The outcomes of every flip in the coins is independent and thus the likelihood of getting a head and tail are equal. The probability of getting a head or tail is thus 1/2. The statement that it is more likely to get tails the next time one flips the coin is thus false. This is because each consecutive coin flip will produce identical outcomes and not decrease or increase the likelihood that another flip will lead to an opposite outcome. The coin that has been flipped three times and comes up heads each time, then it is not more likely that the next flip will result in a tail.
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2. The Rovers play Mustangs. The Rovers can win, loose, or draw, so the probability that they win is 1/3.
The statement is false because the probability could have been 1/3 only when the probability for a win, draw, and loose are all equal likely. However, the given question does not mention that the probability of each outcome is equal. In order to have a purely 1/3 chance of winning, the team mates of each team should be matched equally with the team mate of the opposing team. However, the probability characteristic is impacted in the team because some members of the team can be faster, skillful, or strong. Enhancing these variables in the Rovers team increases the probability that they would win.
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.
The statement is false because it fails to identify the total number of outcomes and permutations for each outcome correctly. When one rolls a die, there are a total of 6 sides which the dice could land on. Therefore, when rolling two dice, the faces cannot be simply added together to come up with 12 different possibilities. Instead the maximum number of outcomes is usually determined by multiplying the number of sides in each die. Multiplying this way would yield 6*6 = 36.
The statement does not include all the addition permutations which can result from rolling the two dice. When we roll the dice two times, the sample space is 36 while the possibilities are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. The sample size is 11 and the chance of getting 6 is 1. The probability of getting a total of 6 is thus 1/11.
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.
The chance of Mr. Purple making 90% is highly dependent upon him and independent on previous statics. The fact 90% of people that have undergone the operation have made a complete recovery is not a statistic which can translate to the likelihood of one individual. The statistics is focused on only two outcomes of success or failure. The statistic that 90% of people that have the operation making a complete recovery only means that 9 out every 10 people that have the operation make a complete recovery. Mr. Purple can make use of this statistic to understand that he has a high chance of recovering from the operation. However, the exact probability of him recovering is dependent on other factors such as his body.
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.
The statement is incorrect because the probability of getting heads or tails is usually determined by multiplying the number of outcomes for each coin. For this case, there is a total of two outcomes per coin which when multiplied 2 times 2 equals 4 total outcomes. The statement leaves out the other outcome of getting a “Tails and Heads.” Correcting the statement, the probability of getting heads and tails is thus 2/4 simplified to 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 .
The idea of a number being unlucky is not based on the rules of probability. The fact that 13 is an unlucky number would thus have no impact on how likely it is for the number to be pulled in an unbiased drawing. The tickets are pulled at random and thus the probability of pulling out number 13 is given by the total number tickets within the raffle.
