1. ## Conditional Probability Help.

Helloooo Statisticians!

I have a question that I believe I can solve but somehow I'm not getting the correct answer. So I'd really appreciate if anyone can point out my mistake for me.

The question is:

The grades of 1st year students were analysed. 70% of the top one quarter of the 1st year had been in the upper 10% of their school, as had 50% of the students in middle half of the 1st year and 20% of the students in the bottom quarter of the 1st year.
a) What is the probability that a randomly chosen 1st year student was in the top 10% of his or her school?
(There are parts b. and c. too but I guess this one is the key.)

My attempt:

......................Top 10%...Not 10%.....Total
Top Quarter.......0.175.......0.075.........0.25
Mid Half.............0.25.........0.25..........0.5
Bottom Quart......0.05.........0.2...........0.25
Total..................0.475.......0.525..........1

So my answer to the question is 0.475. However, the correct answer given is 0.4875.

2. ## Re: Conditional Probability Help.

Easy - if the details you provided are correct then the answer given is incorrect.

3. ## Re: Conditional Probability Help.

Lol okay thank you!!

Also could you help me with this question. Its the last one I promise!

A small commuter airline flies planes that can seat up to 8 passengers. The airline has determined the probability that a ticketed passenger will not show up for a flight is 0.15. For each flight, the airline sells tickets to the first 10 people placing orders. The probability distribution for the number of tickets sold per flight is given in the table below:
No. of tickets...6......7.......8......9.....10
Probability.....0.20..0.35..0.20..0.15..0.10
(c) Assuming independence between the number of tickets sold and the probability a
passenger shows up. For what proportion of flights does the number of ticketed
passengers exceed the number of seats.

My attempt:

0.15(0.85)^9 + 0.1(0.15)(0.85)^9 + 0.1(0.85)^10

Do you think my method is correct?

Thanks a ton!

4. ## Re: Conditional Probability Help.

Close but your middle calculations seems to be off. You're implicitely assuming that when the number of tickets sold is 10 that the probability that only 9 people show up is: 0.15*.85^9 which isn't quite correct. Look at the binomial distribution and see if you can find the discrepancy between your answer and a probability based on the binomial distribution.

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