4.3 (pt. 1)
In a bag containing 10 red marbles, 5 blue marbles, and 3 green marbles, what is the probability of drawing at least one blue marble when drawing two marbles without replacement?
.4784
In a shipment of 20 computers, 5 are defective. What is the probability of finding at least one defective computer if two are selected for inspection?
.4375
In a lottery game, a combination bet is won if you select three numbers, and they can be selected in any order. The lottery has a pool of 30 numbers. What is the probability of winning a combination bet if random number selections are made?
30C3 = 4060
An exam in a Statistics class has 3 versions-blue, yellow and pink. There are 10 blue exams, 5 pink exams, and 10 yellow exams. The instructor places them on the desk before the students get to class. In how many different ways can she arrange these exams?
25!/10!5!10! = 9,816,086,280
A lottery card has a 5% probability of being a win. If you buy 12 cards, find the probability of at least one being a winning card.
.4596
A jar contains 100 candies, of which 20 are chocolate, 30 are caramel, and 50 are mint. If 9 candies are randomly selected from the jar, what is the probability of selecting at least one chocolate candy?
.8658
In a horse race, a quinella bet is won if you select the two horses that finish first and second, and they can be selected in any order. The 140th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinella bet if random horse selections are made?
19C2 = 171
1/171 = .0058
A committee of 5 people needs to be selected from a group of 8 individuals. In how many different ways can the committee be formed if the order in which the members are selected matters?
8P5 = 6720
When rolling a fair six-sided die 8 times, what is the probability of getting at least one 6?
.7674
In a group of 15 friends, what is the probability that at least one of them has a birthday in January, assuming there are 12 equally likely months for birthdays?
.7289
If radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there?
26C2 + 26C3 = 2975
A password for a computer system consists of 5 characters, where each character must be a lowercase letter from the English alphabet. How many different passwords can be created if repetition of characters is not allowed?
26P5 = 7,893,600