A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places.
R <- 54
W <- 9
B <- 75
prob_RorB <- round((R + B) / (R + W + B), 4)
prob_RorB## [1] 0.9348# The probability of randomly selecting a Red or Blue Marble from the box is 0.9348.You are going to play mini golf. A ball machine that contains 19 green golf balls, 20 red golf balls, 24 blue golf balls, and17 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a red golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
G <- 19
R <- 20
B <- 24
Y <- 17
probR <- R / (G + R + B + Y)
prob <- round(probR, 4)
prob## [1] 0.25# The probability of a Red Golf ball is 0.25.A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1399 customers.
What is the probability that a customer is not male or does not live with parents? Write your answer as a fraction or a decimal number rounded to four decimal places.
data <- 81 + 116 + 215 + 130 + 129 + 228 + 79 + 252 + 97 + 72
probMale <- 215/data
probNotmale <- round(1 - probMale, 4)
probNotmale## [1] 0.8463# The probability that a customer selected is not male or does not live with parents is 0.8463Determine if the following events are independent.Going to the gym. Losing weight.
Answer: A)Dependent B)Independent
The two events are dependent.
A veggie wrap at City Subs is composed of 3 different vegetables and 3 different condiments wrapped up in a tortilla. If there are 8 vegetables, 7 condiments, and 3 types of tortilla available, how many different veggie wraps can be made?
veg <- choose(8,3)
condi <- choose (7,3)
tortilla <- 3
wraps <- (veg * condi * tortilla)
wraps## [1] 5880# There are 5880 possible veggie wrapsDetermine if the following events are independent.Jeff runs out of gas on the way to work. Liz watches the evening news.
Answer: A)Dependent B)Independent
The events are independent
The newly elected president needs to decide the remaining 8 spots available in the cabinet he/she is appointing. If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
cabinent <-factorial (14) / factorial(14-8)
cabinent## [1] 121080960A bag contains 9 red, 4 orange, and 9 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 4 jellybeans such that the number of red ones is 0, the number of orange ones is 1, and the number of green ones is 3? Write your answer as a fraction or a decimal number rounded to four decimal places.
R <- choose(9,0)
O <- choose(4,1)
G <- choose(9,3)
combination <- choose((9 + 4 + 9),4)
total <- R * O * G
prob <- round(total/combination, 4)
prob## [1] 0.0459# The probability of choosing 0 red, 1 orange and 3 green jelly beans is 0.0459.Evaluate the following expression.
\(\frac{11!}{7!}\)
exp <- factorial(11)/factorial(7)
exp## [1] 7920Describe the complement of the given event. 67% of subscribers to a fitness magazine are over the age of 34.
67% of subscribers are over 34 years, therefore, 1 - 67% = 33% are 34 or younger.
If you throw exactly three heads in four tosses of a coin you win $97. If not, you pay me $30. Step 1. Find the expected value of the proposition. Round your answer to two decimal places.
probWin <- dbinom(3, size = 4, prob = .5)
probLose <- 1 - probWin
expected = (97 * probWin) - (30 * probLose)
expected## [1] 1.75Step 2. If you played this game 559 times how much would you expect to win or lose? (Losses must be entered as negative.)
outcome <- expected * 559
outcome## [1] 978.25Flip a coin 9 times. If you get 4 tails or less, I will pay you $23. Otherwise you pay me $26.
Step 1. Find the expected value of the proposition. Round your answer to two decimal places.
probWin <- pbinom(4,9, .5)
probLose <- 1 - probWin
expected = (23 * probWin) - (26 * probLose)
expected## [1] -1.5Step 2. If you played this game 994 times how much would you expect to win or lose? (Losses must be entered as negative.)
outcome <- expected * 994
outcome## [1] -1491The sensitivity and specificity of the polygraph has been a subject of study and debate for years. A 2001 study of the use of polygraph for screening purposes suggested that the probability of detecting a liar was .59 (sensitivity) and that the probability of detecting a “truth teller” was .90 (specificity). We estimate that about 20% of individuals selected for the screening polygraph will lie.
liar <- 0.2
truth <- 0.80
liar_sens <- 0.59
truth_sens <- 0.90
pos_det_liar <- liar * liar_sens
false_det_liar <- truth * (1-truth_sens)
actualliar <- pos_det_liar/(pos_det_liar + false_det_liar)
actualliar## [1] 0.5959596# When the polygraph identifies an individual as a liar, there is a 0.596 probability that the individual is actually a liar.pos_det_truth <- truth * truth_sens
false_det_truth <- liar * (1-liar_sens)
actuallytruth <- pos_det_truth/(pos_det_truth + false_det_truth)
actuallytruth## [1] 0.8977556# When the polygraph identifies an individual as a truth teller, there is a 0.898 probability that the individual is actually a truth teller.liarsidentified <- liar + false_det_liar
liarsidentified## [1] 0.28# The probability that a randomly selected individual is actually a liar whether they are identified as a liar by the polygraph or not is is 0.28.