1. A manufacturer puts tires on two cars(four tires each). Each tire has a 10% probability of being flat. Assume the manufacturer puts four tires on one car first, then another four on the second car. What's the probability that one car has no working tires?
2.Let X1, X2...X100 be all independent Bernoulli variables, which take a value of 1 with probability0.5. Estimate the probability that X1,X2,...X100 <60.
For a car, p = 0.1 and n = 4
Probability of all tyres non working = 0.1^4 = 0.0001
Probability that either car has all tyres non working
Required probability = 2C1 * 0.0001 * (1-0.0001) = 0.0002
This is a binomial problem with p = 0.5 and n = 100
lets find the probability P(X < =59)
Required probability = 0.9716