Probability Qn?

Question

1.) A machine produces bolts which are put in boxes. It is known that 1 box in 10 will have at least one defective bolt in it. Assuming that the boxes are independent of eachother, what is the probability that a customer that ordered 3 boxes will get all good bolts?

2.) Suppose that 4% of males are color blind, that 1% of females are color blind, and that males and females make up 50% of the population. If a person ios chosen at random, what is the probability that this person will be color blind?
Can you help in detail....Please

Answer 1

1) From the data we know that the probability of a box having at least 1 defective bolt is 1/10. Therefore the probability of the box having no defective bolts is 9/10. To get 3 boxes that are good, your probability is (9/10)*(9/10)*(9/10) = 72.9%.

2) As males and females make up half the population each, the probability that someone chosen at random is color blind is
probability(person=male)*probability(person=color blind) + probability(person = female)*probability(person=color blind) = 2.5% when you plug in the values.

Answer 2

1. p= 9/10 * 9/10 * 9/10 = 729/1000=0.729

2. p= ( 4/100 + 1/100 ) * 1/2 = 1/20 * 1/2 = 0.025