A
The probability that a randomly selected student arrives late is 0.18. What is the probability that the student does not arrive late?
The probability that a randomly selected student arrives late is 0.18. What is the probability that the student does not arrive late?
1 - 0.18 = 0.82
A fair spinner has eight equal sections, three of which are red. What is the probability of landing on red?
A fair spinner has eight equal sections, three of which are red. What is the probability of landing on red?
3/8 or 0.375
Events A and B are mutually exclusive. If P(A) = 0.35 and P(B) = 0.28, find P(A Union B).
Events A and B are mutually exclusive. If P(A) = 0.35 and P(B) = 0.28, find P(A Union B).
P(A Union B) = 0.35 + 0.28 = 0.63
A basketball player makes 30% of her three-point attempts. Using random digits 0-9, give an appropriate assignment for simulating one attempt.
A basketball player makes 30% of her three-point attempts. Using random digits 0-9, give an appropriate assignment for simulating one attempt.
0, 1, 2: made shot
3,4,5,6,7,8,9: missed shot (different possible answers)
Suppose P(A) = 0.55, P(B) = 0.4, and P(A intersect B) = 0.2. Find P(A union B).
Suppose P(A) = 0.55, P(B) = 0.4, and P(A intersect B) = 0.2. Find P(A union B).
0.55 + 0.40 - 0.20 = 0.75
Of 30 students who participate in a school sport, 18 also belong to a club. If a student who participates in a sport is selected, what is the probability that the student belongs to a club?
Of 30 students who participate in a school sport, 18 also belong to a club. If a student who participates in a sport is selected, what is the probability that the student belongs to a club?
P(Club | Sport) = 18/30 = 0.60.
Two fair coins are tossed. What is the probability of obtaining at least one head?
Two fair coins are tossed. What is the probability of obtaining at least one head?
1 - P(no heads) = 1 - (1/2)2 = 3/4
Suppose P(A) = 0.4, P(B) = 0.5, and P(A intersect B) = 0.2. Are A and B independent?
Suppose P(A) = 0.4, P(B) = 0.5, and P(A intersect B) = 0.2. Are A and B independent?
Yes, because P(A)*P(B) = (0.4)(0.5) = 0.2
A bag contains five red marbles and seven blue marbles. Two marbles are selected without replacement. What is the probability both are red?
A bag contains five red marbles and seven blue marbles. Two marbles are selected without replacement. What is the probability both are red?
(5/12)(4/11) = 5/33 or ~0.152
In a group of 120 students, 48 ride the bus. Of the bus riders, 18 arrived late. Find the probability that a student arrived late, given that the student rides the bus.
In a group of 120 students, 48 ride the bus. Of the bus riders, 18 arrived late. Find the probability that a student arrived late, given that the student rides the bus.
P(late|bus) = 18/48 = 0.375
A machine produces a defective item 20% of the time. Assuming independence, what is the probability of obtaining exactly 2 defective items among 10 items?
A machine produces a defective item 20% of the time. Assuming independence, what is the probability of obtaining exactly 2 defective items among 10 items?
(10 choose 2)*(0.2)2(0.8)8 = 0.302
Benson is playing a game that gives him a net gain of $5 with probability 0.2 and net loss of $1 with probability 0.8. What is his expected net gain per game?
Benson is playing a game that gives him a net gain of $5 with probability 0.2 and net loss of $1 with probability 0.8. What is his expected net gain per game?
E(X) = 5(0.2) + (-1)(0.8) = $0.20
A disease affects 2% of the population. A test correctly gives a positive result to 95% of people with the disease and incorrectly gives a positive result to 8% of people without it. What is the probability that a randomly selected person tests positive?
A disease affects 2% of the population. A test correctly gives a positive result to 95% of people with the disease and incorrectly gives a positive result to 8% of people without it. What is the probability that a randomly selected person tests positive?
(0.02)(0.95) + (0.98)(0.08) = 0.0974 or ~1%.
Harry's factory produces 60% of a company's products and has a 3% defect rate. Jerry's factory produces the remaining 40% and has an 8% defect rate. A randomly selected product is defective. What is the probability it came from Jerry's factory?
Vicky's factory produces 60% of a company's products and has a 3% defect rate. Jane's factory produces the remaining 40% and has an 8% defect rate. A randomly selected product is defective. What is the probability it came from Jane's factory?
P(J|D) = [(0.4)(0.08)] / (0.6)(0.03) + (0.4)(0.08) = 0.64
Suppose 65% of BBSZ students support a no-curve grading policy. 12 students are selected randomly. Find the probability that exactly 9 support the policy.
Suppose 65% of BBSZ students support a no-curve grading policy. 12 students are selected randomly. Find the probability that exactly 9 support the policy.
(12 choose 9)*(0.65)9(0.35)3 = ~0.195