1. Probability help

Hey guys can anybody help me with my probability i need to get the working to help me with my sac:

1.Three people are to be randomly chosen from a football playoff game to recieve prizes, 70% of the supporters are eagles fans:
find pr
a) 1 of the winners is an eagles fan
b) the mean and the variance

2.A group of people watched a movie at a premiere nd were asked to rate the movie, good awful or bad. If 10 of 100 rate the movie awful find pr that at least one of them will be included in a sample of 3 to comment on the movie.

2. Originally Posted by RoboStar
Hey guys can anybody help me with my probability i need to get the working to help me with my sac:

1.Three people are to be randomly chosen from a football playoff game to recieve prizes, 70% of the supporters are eagles fans:
find pr
a) 1 of the winners is an eagles fan
b) the mean and the variance

2.A group of people watched a movie at a premiere nd were asked to rate the movie, good awful or bad. If 10 of 100 rate the movie awful find pr that at least one of them will be included in a sample of 3 to comment on the movie.
1. Let X be the random variable number of eagles fan winners.

X ~ Binomial(n = 3, p = 0.7) (assuming the 3 people are chosen from a 'large' group).

You should know what to do from here.

2. Let Y be the random variable number of people who rated the movie awful.

Technically the exact probability is $\displaystyle \Pr(Y \geq 1) = 1 - \Pr(Y = 0) = 1 - \frac{{10 \choose 0} \cdot {90 \choose 3}}{{100 \choose 3}} = \frac{67}{245}$.

An approximate solution would consider Y ~ Binomial(n = 3, p = 1/10) (since 100 is large).

Then calculate $\displaystyle \Pr(Y \geq 1) = 1 - \Pr(Y = 0)$.

I doubt you'll find a lot of difference between the two answers in the first two or so decimal places.

3. Thanks for that man, Ive only got 2 more problems that I need help with one involving normal distrubutions I have had trouble trying to interpret the question with unknowns and another binomial question:

1. Let X be a normally distributed variable with mean = u and standard deviation = o. If u < a< b and Pr(x > b) = q
a) Pr(a < x < b)
b) Pr(-b < x < -a)
c) Pr( x > b | x > a)

2. In order to asses the quality of video games being produced the manufacturer selects 10 games at random before they are boxed for delivery, they are inspected.
a) If it is known 8 % of games are defective find:
i) probability that one of the games on the sample will be defective.
ii) that at least one of the games in the sample are defective.
iii) one of the games in the sample will be defective, given that least one of the games are defective