Probability Formulas
The formula of the general addition rule.
What is P(A or B) = P(A) + P(B) - P(A int B)
At coffee shop there are light, median, and dark roast. The prob of being a light roast is .15 and .25 for dark roast for a given day. What is the prob of the coffee of the day NOT being a light roast or dark roast?
What is 0.60
At a local elementary school, 35% of all students have brown eyes, 45% brown hair, and 60% have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event of having brown eyes and H represent the event of having brown hair. Are E and H mutually exclusive events?
The random variable X has a mean of 12 and s.d. of 3. The random variable W is defined as W = 7 + 2X. What are the mean and standard deviation of W?
What is mean = 31 and s.d = 6
It is known that 75% percent of all households in the US have intermittent internet connectivity problems. For random samples of 450 independent households in the US. What are the mean and standard deviation of the number of households that have intermittent internet connectivity problems?
mean= 450*.75
sd = sqrt(450*.75.25)
The formula of the general multiplication rule.
What is P(A and B) = P(A)*P(B|A)
Consider rolling two dice. The dice are rolled and the sum of the numbers landing face up will be recorded. Let the event E represent the event of rolling a sum of 5. How many outcomes are in the collection for event E?
What is four
Given independent events D and E such that P(D) = .6 and P(D and E) = .18, which of the following is a correct ?
A) P(E) = .12
B) P(E) = .4
C) P(D or E) = .28
D) P(D or E) = .72
E) P(D or E) = .9
What is D
At a certain bakery the price of each donut is $1.50. Let the random variable D represent the number of donuts a typical customer purchases each day. The expected value and variance of D are 2.6 donuts and 3.6 donuts2 respectively. Let random variable P represent the price of donuts a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of P?
What is $2.85
A blind test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the prob that at least 8 of the 9 participants will correctly identify the tap water?
What is 0.0195
The formula for conditional probability
What is P(A|B) = P(A and B) / P(B)
A high school theater club has 40 students, of whom 6 are left handed. Two students from the club will be selected at random. one at a time without replacement. What is the probability that the 2 students selected will both be left-handed?
What is 30/1560 = .019
A company believes that:
-> The prob of event A is .75
-> The prob of event B is .5
-> The prob of event (A and B) is .375
If this belief is correct, which of the following is true?
A) A and B are mutually exclusive and independent
B) A and B are mutually exclusive and not independent
C) A and B are not mutually exclusive and independent
D) A and B are not mutually exclusive and not independent
E) A and B are not mutually exclusive and independence can not be checked.
What is C.
A charity raffle is planned, there are 2000 tickets that are sold for $1. The holders of 32 winning tickets will each win a prize. There 20 tickets ($25 prize), 10 tickets ($50), and 2 tickets ($300). The random variable W represents the value of the prize won for a single ticket minus the cost of the ticket. What is the expected value of W?
What is -$0.20
To start her own lawn mower, Rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20% chance of starting. What is the probability that it takes more than 2 tries?
What is .64
The formula to check for mutually exclusive events.
What is P(A or B) = P(A) + P(B)
or
P(A and B) = 0
At a large high school 40$ of the students walk to school, 32% have been late to school at least once, and 37.5% of students who walk to school have been late to school at least once. If a student is selected at random what is the probability the student will be one who both walks to school and has been late to school at least once?
What is 0.15
The prob that a particular component operates successfully is 3/4. and electrical system consists of three such components that operate independently. The system will function successfully if at least one of the three components operates successfully. What is the prob that the system will function successfully?
What is 63/64
A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let random variable X be the amount won from the selection of the chip and W be the total amount won, where W = X - 15. What is the mean of W?
What is -$4.50
Ten percent of all Dynamite Mints candies are orange and 45% of all Holiday Mints candies are orange. Two independent random samples, each of size 25 are selected from both candies separately. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples combined?
What is 13.75 and 2.905
The formula to check for independent events
What is P(A and B) = P(A)*P(B)
While investigating customer complaints, the customer relations department of Sonic Air found that 15% of the flights arrive early and 25% arrive on time. Additionally, 65% of the flights are overbooked, and 72% are late or not overbooked. One Sonic Air flight will be selected at random. What is the prob that the flight selected will be late and not overbooked?
What is 0.23
Clark drives through two traffic lights on his way to work. From experience, he estimates that the prob that the first light will be red when he reaches it is .3. He also estimate that the prob that the second light will be red when he reaches it is .45. The lights are far enough apart that they can be considered to operate independently of each other. What is the prob that at least one of the two lights will be red on a randomly selected drive to work?
What is 0.615
A company ships gift baskets that contain apples and pears. The distributions of weight for the apples, the pears, and the baskets are each approximately normal. The mean and s.d. of each are as follows. Apple(mu = 4.72, sd = .2), Pear (mu = 5.41, sd = .18), Basket(mu = 13.25, sd = 1.88). The weights are assumed to be independent. Let the random variable W represent the total weights of 4 apples, 6 pears, and 1 basket. Which of the following is closest to the standard deviation of W?
What is 1.97
Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends' scores are approximately normal. Where andy has mean score of 150 with a s.d. of 30, and Bob has a mean score of 165 with a s.d. of 15. Assuming that their scores are independent, which of the following values is closest to the probability that andy will have a greater score than bob in a single game?
What is 0.33