Probablity Question

Stanford

Is anybody here knowledgable in the area of numbers and probability, I'm sstruggling with a LCOL problem?

KaneToad

https://www.boards.ie/discussion/2058331273/probablity-question

The chances of me being any help to you are low.

But, hopefully my reply will entice in some others more knowledgeable on the topic!

zv2

https://www.boards.ie/discussion/2058331273/probablity-question

Why not post the problem? Better chance of an answer.

Stanford

Good idea, its a Leaving Cert Ordinary level question but something is not quite right

Three passengers who did not survive a plane crash are to be awarded bravery medals posthumously , Each person can only get one medal and all three medals are different,

1. In how many different ways can the medals be assigned
2.  If the three passengers were given the same medal would the number of outcomes be different from that in 1. above? Why/why not?

If the probability that a passenger chosen was in first class is  0.4

What is the probability that

 

1.   The passenger chosen first was in first class

 

2.   All three passengers chosen were in first class

 

3.   At least one passenger chosen was not in first class

Michael Collins

https://www.boards.ie/discussion/comment/121619821#Comment_121619821

The question is badly phrased. Did you copy it word-for-word? It's not completely clear if each person must get a different medal, or if there are 3 distinct medal types which can be given out multiple times.

Since Q2 suggests the same medal can be given out multiple times, so I'll go with that assumption.

Q1. Each person can be given one of three different medals, so there are 3 x 3 x 3 = 27 possible arrangements.

Q2. Yes, if they all must be given the same medal then we have 3 x 1 x 1 = 3 possible arrangements.

For the probabilities

Q1. Assuming any given passenger has 0.4 probability of being in first class, then the first such passenger chosen has this probability of being in first class i.e. 0.4.

Q2. There's really no way to answer this, as we are not told that the passengers are chosen independently of each other. And, in principle, if this were a real scenario, since the same person can't be chosen twice, if the first passenger chosen is in first class then there are fewer passengers left in first class so this should affect the probability of the next passenger being in first class. Not to mention that they all died, which might indicate there were in the same section of the plane!

Q3. Same problem as above.

If we ignore this, and assume each passenger is chosen independently (somehow), then

Q2. 0.4 * 0.4 * 0.4 = 0.064

Q3. Since either all passengers are in first class, or at least some are not, we have:

P(all in 1st class) + [P(exactly one not in first class) + P(exactly two not in first class) + P(exactly three not in first class)] = 1

=> P(all in 1st class) + [P(at least one not in first class)] = 1

=> P(at least one not in first class) = 1 - P(all in 1st class) = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936