Mathematical odds of occurring? Factual happenings, (All random).?

Question

4 situations and what are their chances of happening? :
1.The 3 letters on a license plate have the sequence of L J D in order(my wife's first initial and the initials her brother-in-law who gave her the car is known by) when the number of letters can total only 3 and the "Os" from the alphabet are not used.
2. If a roster of names of members of an organization numbers a total of 110 names; what are the chances of the same name being drawn TWICE-in-a-row with all the names are included both times? This happened to me at our organizations 50-50 drawing on 2 consecutive month's drawings! (I would have won about $100 the first time if I had been present and when I was told that in my absence my name was drawn, I attended the next month's meeting and won $100 plus!)
3. Our area has 15 different 3-numbered prefixes, The chances of having the same last 4 numbers alike in the same order as an associate?
4.COLEMAN camper plate with 4 #s the same as his former home address:EX:5475 Coleman

I should have mentioned for event #3 that I was discussing phone numbers! Sorry!

I think mathgirl meant 1 in 9999 for the first part, (thats the way it occurred), but doesn't the fact that the name of the street being Coleman change the odds dramatically?

Answer 1

There is a difference between odds and probability. Each time your number was drawn you had a 1 in 110 Chance of winning. After having your number drawn the one month, the odds it would be drawn the second month were still 1 in 110.

If you were betting that your number would be drawn both times, the odds are 1 in 12 100.

The chance of having an L as the first character, 1 in 25.
The chance of having an LJ as the first two characters, 1 in 625.
The chance of having an LJD as the first three characters, 1 in 15625.

The prefix answer is 15 in 10 000.

1 in 10 000

The name coleman on the street would make the odds astronomical since you would be adding 10's or hundreds of thousands of possibilities into the equation.

By the way 4 digits give you 10 000 not 1 thousand.

Answer 2

1. The probability is (1/25)^3 = 0.00640%

2. The probability is (1/110)^2 = 0.00826%

This is the probability that it will happen in the next two drawings. The probability that it will happen in two successive months is greater. For example, if there were three meetings, then you have the possibility that it will happen in the first and second meeting , but you also have the possibility that it could happen in the second and third meeting. If there is a meeting every month for several years in a row -- it is likely that it will happen to someone twice in a row. There are people who have won multimillion dollar lotteries twice. There is actually a high probability that this will happen to someone -- but a very remote possibility that it will happen to you.



3 & 4 are both have a probability of 1/1000 (0.10%)

Answer 3

1) Since the O's are not used, then there are only 25 letters to choose from.
There will be 25*25*25 = 25^3 different 3 letter license plates.
LJD can only occur in one way.
Therefore, the probability is
1/25^3 = 1/15625 = 0.000064
2) P(happens 1st drawing) = 1/110
P(happens 2nd drawing) = 1/110
P(happens 1st and 2nd drawing)
= P(happens 1st drawing)P(happens 2nd drawing)
because the events are independent.
(1/110)(1/110) = 1/12100 = 0.000082644628
3) I don't quite understand this one.
4) Do the numbers have to be in the exact same order? or do the same numbers just have to appear in any order, like 4755?
If it's the first one, then the answer is 1/1000 = 0.001
If it's the second one, then it is
12/1000 = 0.012

Answer 4

1. 1 in 15625 of all 3 character length license plates. assuming you can use numbers and O's. In reality, combinations like A$$ won't be allowed due to profanity.

2. It's 1 in 110 for this to happen to anyone on the roster.

3. 1 in a 1000. Assumming 0000 is used.

4. 1 in 1000.