Complete the below:
Q1. Each vehicle in Mexico is either a truck, car or bicycle. Also each vehicle is red, green or yellow. We pick a vehicle at random. The following are known facts:
1. There's a 30% chance that vehicle is truck
2. There's 50% chance that vehicle is red
3. There's 20% chance that vehicle is a red truck
4. The vehicle is more likely to be a yellow truck than a green car
a. If we select a vehicle at random. What is the probability that it is red or a truck?
b. if we select a vehicle at random, what is the chance that it is neither red nor a truck?
c. if we select 100 vehicles, how many would be yellow or green?
d. let's say we select a vehicle at random. Show that the probability that the vehicle is either yellow or a bicycle is at least 0.4.
Q2. There are 75% guys & 25% girls in a class.
On a particular day, each guy has 40% chance of missing class & girl has 20 % chance of missing class.
a. What is the probability that a randomly chosen student is a girl and is not in class today?
b. What is the probability that a randomly chosen student will miss class today?
c. What is the probability that a randomly chosen student who is in class today is a girl?
Q3. How do you prove the following?
1. P (A+B+C) <= P (A) + P (B) + P(C) - 2P (ABC)
2. P (CD) <=P(C)
Q4. Consider an except that has n (finite) number of outcomes.
In how many ways can we choose n-1 of the 2^n events, so that the probabilities of all 2^n events can be computed from the n-1 known probabilities.