Probability Exam Questions
1) The chance of an event A is 30%; the chance of event B is 50%
a) Assuming the events are independent, the chance that both events happen is ______%.
b) Assuming the events are mutually exclusive, the chance that either event happens is ________%
2) You have a deck of card with 52 cards. A card is drawn.
a) What is the probability the card is black?
b) What is the probability that the card is a spade?
c) What is the probability that the card has the number 2, 3, 4, 7 or 8?
d) What is the probability the card is an Ace?
e) What happens in the questions a through d if two jokers are added to the deck?
3) A six-sided die is rolled three times, what is the probability of rolling three identical results?
4) A six-sided die is rolled seven times, what is the probability of rolling two 4s?
5) An eight-sided die is tossed 10 times. What is the probability of never getting a 5?
6) A four-sided dice is tossed twice, what is the probability of rolling a 4?
7) A coin is tossed 1,000 times and there are 550 heads.
a) Please compute the binomial probability of tossing up to and including 549 heads. What is it?
b) Now please calculate the probability of tossing 550 heads and over.
c) Based on these results, do you think the coin is fair?
8) A box contains one red marble, three green marbles and six blue ones. You take marbles out of the box one at a time and keep them.
a) If you take one marble, what is the probability it is blue?
b) If you take two marbles, what is the probability both are green?
c) If you take three marbles, what is the probability one is red, blue and green?
d) If you take two marbles, what is the probability one is either blue or red?
e) If you take two marbles, what is the probability that you do not pick a blue marble?