David W. answered • 05/08/15
Tutor
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Daniel W. enumerated a list of possibilities, but did not explain (statistically) the concepts involved. Also, he did not explain how he counted cases to answer the event questions (Note: in math, concepts and applications must be taught as well as calculations and procedures).
Concept:
(1) For an ordinary (fair) die, it is equally probable that each of the sides (1 to 6) will face up on the first roll (With first rolls of lots of dice, the frequency distribution of 1-6 will be uniform).
(2) No matter what face the first roll shows, the probabilities of the second roll showing 1-6 will also be uniform (physically, they are not connected to each other).
Procedure:
The probability of Event A (Sum > 6) happening is the ration of (the count of events in which the condition is true) divided by (the total count of possible events). That is why 21/36 and 18/36 appears.
Later, in Statistics, you will learn formulas that can be used when more dice are rolled or when you would like to consider other Events.
Applications (don’t answer, just recognize that your problem might be useful in these cases):
(1) If the population has the same number of boys as girls (equal likelihood of occurrence), how likely is it that a family will have all boys (2 or more)?
(2) How many people must be in a room before the likelihood that two of them have the same birthday exceeds 90% ?
(3) If two tennis players are just as likely to win each point, how likely is it that a player can win the match after being a set down?
Concept:
(1) For an ordinary (fair) die, it is equally probable that each of the sides (1 to 6) will face up on the first roll (With first rolls of lots of dice, the frequency distribution of 1-6 will be uniform).
(2) No matter what face the first roll shows, the probabilities of the second roll showing 1-6 will also be uniform (physically, they are not connected to each other).
Procedure:
The probability of Event A (Sum > 6) happening is the ration of (the count of events in which the condition is true) divided by (the total count of possible events). That is why 21/36 and 18/36 appears.
Later, in Statistics, you will learn formulas that can be used when more dice are rolled or when you would like to consider other Events.
Applications (don’t answer, just recognize that your problem might be useful in these cases):
(1) If the population has the same number of boys as girls (equal likelihood of occurrence), how likely is it that a family will have all boys (2 or more)?
(2) How many people must be in a room before the likelihood that two of them have the same birthday exceeds 90% ?
(3) If two tennis players are just as likely to win each point, how likely is it that a player can win the match after being a set down?
