1. ## Fractions

Greetings,

I'm in need of some help, I don't understand what this question wants me to do.

"In a course on probability and statistics, a students learns that when rolling a pair of dice, the probability of getting a 5 is 1/9, and the probability of getting a 6 is 5/36. Does getting a 5 or a 6 have a greater probability? Explain."

This is in my textbook and we have only covered comparing and simplifying fractions, however, I think this is asking for more than what we have learned. Any advice on what this is asking would be appreciated, thank you.

2. Originally Posted by JMiller
Greetings,

I'm in need of some help, I don't understand what this question wants me to do.

"In a course on probability and statistics, a students learns that when rolling a pair of dice, the probability of getting a 5 is 1/9, and the probability of getting a 6 is 5/36. Does getting a 5 or a 6 have a greater probability? Explain."

This is in my textbook and we have only covered comparing and simplifying fractions, however, I think this is asking for more than what we have learned. Any advice on what this is asking would be appreciated, thank you.
1/9 - 5/36 = ??

5/36 - 1/9 = ??

3. Originally Posted by JMiller
Greetings,

I'm in need of some help, I don't understand what this question wants me to do.

"In a course on probability and statistics, a students learns that when rolling a pair of dice, the probability of getting a 5 is 1/9, and the probability of getting a 6 is 5/36. Does getting a 5 or a 6 have a greater probability? Explain."

This is in my textbook and we have only covered comparing and simplifying fractions, however, I think this is asking for more than what we have learned. Any advice on what this is asking would be appreciated, thank you.
The question is just asking you to compare fractions. You can restate it as "Is 1/9 or 5/36 a greater number?" If your answer is 1/9, then 5 has a greater probability.

4. Originally Posted by JMiller
Greetings,

I'm in need of some help, I don't understand what this question wants me to do.

"In a course on probability and statistics, a students learns that when rolling a pair of dice, the probability of getting a 5 is 1/9, and the probability of getting a 6 is 5/36. Does getting a 5 or a 6 have a greater probability? Explain."

This is in my textbook and we have only covered comparing and simplifying fractions, however, I think this is asking for more than what we have learned. Any advice on what this is asking would be appreciated, thank you.
You have not said what you are studying, but it sounds like arithmetic so I am guessing that you have not studied either algebra or probability theory. You do not need to have studied either to answer the question. A probability is a number, zero, one, or a fraction between zero and one, assigned to an event, e.g. rolling two fair dice so that the sum of the spots face up is equal to five. If the event is impossible, the number assigned is zero. If the event is certain, the number assigned is one. If the event is possible but not certain, the number assigned is a fraction between zero and one, and the bigger the fraction, the more likely is the occurrence of the event."

So by comparing the fractions assigned to two different events, the one with the higher number is more likely to happen (is more probable).

5. The original question requires no knowledge of probability; JMiller, you don't need to pay attention to what has been said about it unless it interests you.

But if you are interested in where the two given fractions come from, they arise because there are 36 possible outcomes (ordered pairs) for a pair of dice; of those,

• the sum is 5 for four of them, namely (1,4), (2,3), (3,2), and (4,1), for a probability of 4/36 = 1/9
• the sum is 6 for five of them, namely (1,5), (2,4), (3,3), (4,2), and (5,1), for a probability of 5/36.

Saying that actually gives you a little extra help in answering the real question, namely whether 1/9 or 5/36 is larger. Can you see why?

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