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Probability Questions

WHICH ANSWER IS RIGHT 1, 2, OR 3 AND WHY?

There is a 20% probability of a rain tomorrow means that:
1. Tomorrow it will be raining during 0.2 of the day, and the rest of the day it will be clear;
2. Out of the next 5 days, one day it will be raining ;
3. According to the records, if a weather like one we have today occurred in the past, then in 20% of cases it was raining on the next day.

WHAT IS WRONG AND WHY?

You bought 10 lottery tickets. One of them won a prize. That means that the probability of winning a prize is 1/10.

TRUE OR FALSE AND WHY?

1. In a lottery, the more tickets you buy, the more chance you have to win the prize(s).
2. If you have 3 suits, 10 shirts, and 12 neckties, you can come to work each time in a different outfit during the whole year.

FOR DISCUSSION DEVELOPMENT (IF YOU CAN GIVE ME A FORMULA OR METHOD OF SOLVING THIS TYPE OF PROBLEM I CAN COME UP WITH THE BIBLICAL ACCOUNT).

We know, as Christians, that numerous major prophecies of the Old Testament were fulfilled by Jesus Christ. As a class, we will compute the probability of Christ fulfilling all the prophecies you can identify (i.e., compute P(A and B and C and . . .)). There are more prophecies than students in this section. Thus, each student should provide a brief statement of one prophetic event, with both an Old and New Testament scripture reference of a prophecy fulfilled, and the probability you want to assign that event. Some probabilities will be straightforward; others will not, so give it your best shot with justification. We will assume all events are independent. Any bible with a section on messianic prophecies fulfilled will be helpful.

Example:
Christ was to be born in Bethlehem. O.T. Micah 5:2. N.T. Luke 2:4, 7 (listed below for your information only)
O.T. Micah 5:2
But thou, Beth-lehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting.
N.T. Luke 2:4, 7
And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem, (because he was of the house and lineage of David:)
And she brought forth her firstborn son, and wrapped him is swaddling clothes, and laid him in a manger; because there was no room for them in the inn.

What is the probability of Christ being born in Bethlehem? Let's say at the time of Micah there were about 100 cities in the area that could have been identified. Thus, Christ being correctly born in Bethlehem would have a 1 in 100 chance of occurring, or a probability of 0.01.

These questions require logical reasoning, so don't answer them with just "true" or "false" but give justification.

Solution Preview

WHICH ANSWER IS RIGHT 1, 2, OR 3 AND WHY?
There is a 20% probability of a rain tomorrow means that:
1. Tomorrow it will be raining during 0.2 of the day, and the rest of the day it will be clear;
2. Out of the next 5 days, one day it will be raining ;
3. According to the records, if a weather like one we have today occurred in the past, then in 20% of cases it was raining on the next day.

Answer:

#3 is right. When we say "20% chance of rain" that means that there is a 20% chance that there will be rain anywhere in the area at some time tomorrow.

If #1 was true, then forecasters would generally say that there was a 100% chance of rain because rain would definitely fall at least some time during the day.

If #2 were true, forecasters would probably say something like "there is a 100% chance of rain at least once in the next 5 days".

#3 shows that you need to look at the specific conditions to make predictions about coming events.

WHAT IS WRONG AND WHY?
You bought 10 lottery tickets. One of them won a prize. That means that the probability of winning a prize is 1/10.

Answer:

This is false. What if a total of 1000 tickets were sold (you happened to buy ten of them). Since one ticket ...

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