Independent Probability
If you flip a coin what's the probability of getting heads?
1/2
A bag has 12 red marbles and 13 blue marbles. If you pick 2 marbles one after the other without replacement, Find out P(one each color)
13/25
A spinner with 4 equal sections labeled 1,2,3,4. If you spin a 4, you gain $20. If you spin a 2, you get $12. Otherwise you lose $16. What is EV? Is it a fair game?
It is a fair game because EV=0
Peyton Manning averaged 259 passing yards per game while playing with the Colts with a standard deviation of 74 yards. What two values make up 68% of the data ?
185-333
P(joined in January)=0.12
P(member for over 6 months)=0.5
P(over 6 months and January)=0.024
Find the probability that a client remained a member for more than 6 months, given that the client joined in January.
P(over 6 months ∣ January)= 1/5 or 0.2
1/4
A bag has 12 red marbles and 13 blue marbles. If you pick 2 marbles one after the other without replacement, Find out P(at least one blue)
39/50
You participate in a game show in which you respond to questions that have 3 possible answers. You gain $10 for each correct answer, and lose $6 for each incorrect answer. Every question must be answered. If you do not know the answer to one of the questions, is it to your advantage to guess the answer?
No because EV= -2/3 , you lose points by guessing
Peyton Manning averaged 259 passing yards per game while playing with the Colts with a standard deviation of 74 yards. What is the z-score for 285?
26/74 = 0.35
P(for men)=0.55
P(botanic scent)=0.18
P(for men and botanic)=0.05
Find the probability that a deodorant is for men, given that it has a botanic scent.
P(for men ∣ botanic)= 5/18
1/3
A jar contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be blue and the second will be blue as well?
6/91
If you pay $3 to play, you get $10 for getting spade, if not you lose all money. Is this fair? What is the EV?
EV: $-0.50 , player loses 50 cents per game , not fair
Tiger Woods has an average driving range of 304 yards with a standard deviation of 8. What percent of data is greater than 315?
8.5%
In a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. If a car buyer chosen at random bought an alarm system, what is the probability they also bought bucket seats?
50%
1/4
In a class of 7, there are 4 students who play soccer.
If the teacher chooses 3 students, what is the probability that none of the three of them play soccer?
1/35
The game costs $20. You draw one card from a standard deck of playing cards. If you pick a Red Ace, you will win $100. If you pick a King card, you win $80. If you pick any other card you lose $10. Do you want to play? Why or Why not.
No because EV is $-18.85 (less than the cost)
Tiger Woods has an average driving range of 304 yards with a standard deviation of 8. What percent of the data is less than 310?
77.3 %
The probability that a randomly selected student from a college is a senior is .20. The joint probability that the student is a computer science major AND a senior is .03. Find the conditional probability that the student selected is a computer science major given he/she is a senior.
P(Computer Science | Senior) =
.03 / .20 = .15 = 15%
5/12
A jar contains 6 red jelly beans, 6 green jelly beans, and 6 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be green and the second will be green as well?
5/11
Ten red marbles and 15 blue marbles are in a bag. A game is played by first paying $5 and then picking two marbles out of the bag without replacement. If both marbles are red you are paid $10. If both marbles are blue, you are paid $5. If the marbles don't match, you are paid nothing. Determine whether or not is it to your advantage to play.
No, because EV= $-1.75 (less than the cost)
A study of elite distance runners found a mean body weight of 63.1 kilograms (kg), with a standard deviation of 4.8 kg. What proportion of runners have body weights below 60 kg?
25.92%
They're 5 red chip, 4 blue chips, and 6 white chips in a basket. Two chips are randomly selected. Find the probability that the second chip is red given that the first chip is blue. (Assume that the first chip is not replaced.)
P(selecting a chip | first chip blue) = 5/14