total <- 54+9+75
p_red <- 54/total
p_white <- 9/total
p_blue <- 75/total
paste("The probabilty of picking a red or blue marble is",round(p_red+p_blue,4))## [1] "The probabilty of picking a red or blue marble is 0.9348"golf_total <- 19+20+24+17
golf_green <- 19/golf_total
golf_red <- 20/golf_total
golf_blue <- 24/golf_total
golf_yellow <- 17/golf_total
paste("The probabilty of picking a red golf ball is",round(golf_red,4))## [1] "The probabilty of picking a red golf ball is 0.25"pizza_total <- 81 + 116 + 215 + 130 + 129 + 228 + 79 + 252 + 97 + 72
paste("The probabilty that the customer is not male and lives with his parents is",round(1 - (215/pizza_total),4))## [1] "The probabilty that the customer is not male and lives with his parents is 0.8463"Going to the gym and losing weight are dependent events.
veggies <- choose(8,3)#pick 3 of 8 veggies
condiments <- choose(7,3)#pick 3 of 7 condiments
tortilla <- choose(3,1)#pick 1 of 3 tortillas
total_wraps <- veggies*condiments*tortilla
paste("Total number of wraps to chose from is",total_wraps)## [1] "Total number of wraps to chose from is 5880"Jeff running out of gas on the way to work and Liz watching the evening news are independent events.
perm = function(n, x) {
factorial(n) / factorial(n-x)
}
paste("The number of different ways the memeber of the cabinet can be appointed are", perm(14,8))## [1] "The number of different ways the memeber of the cabinet can be appointed are 121080960"jelly_red <- choose(9,0) #get 0 of 9 red jellybeans
jelly_orange <- choose(4,1) #get 1 of 4 orange jellybeans
jelly_green <- choose(9,3) #get 3 of 9 orange jellybeans
jelly_total <- choose(22,4)#get 4 of 22 total jellybeans
jelly_prob <- (jelly_green*jelly_orange*jelly_red)/jelly_total
paste("The probability of getting 0 red, 1 orange, and 3 green jellybeans is",round(jelly_prob,4))## [1] "The probability of getting 0 red, 1 orange, and 3 green jellybeans is 0.0459"paste('11!/7!=',factorial(11)/factorial(7))## [1] "11!/7!= 7920"The compliment of 67% of subscribers being over the age of 34 is 33% of subscribers are 34 or younger.
heads <- pbinom(3, 4, 0.5) - pbinom(2, 4, 0.5)
paste("Probabilty of 3 heads is",heads)## [1] "Probabilty of 3 heads is 0.25"ev <- (97*heads) - (30*(1-heads)) #win - lose
paste("Expected value is",ev)## [1] "Expected value is 1.75"ev_win <- 559*ev
paste("If I play 559 times I can expect to win",ev_win)## [1] "If I play 559 times I can expect to win 978.25"tails <- pbinom(4, 9, 0.5)
paste("Probabilty of 4 tails or less is",tails)## [1] "Probabilty of 4 tails or less is 0.5"ev2 <- (23*tails) - (26*(1-tails)) #win - lose
paste("Expected value is",round(ev2,4))## [1] "Expected value is -1.5"ev2_win <- 994*ev2
paste("If I play 994 times I can expect to lose",abs(round(ev2_win,4)))## [1] "If I play 994 times I can expect to lose 1491"p_liar <- .2
p_truth <- .8
p_sens<- .59
p_spec <- .9
#probabilty of liar given that the polygraph detected
#P(liar | positive test) / P(liar | positive test) + P(truth | positive test)
p_liar_sens <- (p_liar*p_sens) / ((p_liar*p_sens) + (p_truth*(1-p_spec)))
paste("The probabilty that an individual is a liar given that the polygraph detected is",round(p_liar_sens,4))## [1] "The probabilty that an individual is a liar given that the polygraph detected is 0.596"#probabilty of truth teller given that the polygraph detected
#P(truth | negative test) / P(truth | negative test) + P(liar | negative test)
p_liar_sens <- (p_truth*p_spec) / ((p_truth*p_spec) + (p_liar*(1-p_sens)))
paste("The probabilty that an individual is a truth-teller given that the polygraph detected is",round(p_liar_sens,4))## [1] "The probabilty that an individual is a truth-teller given that the polygraph detected is 0.8978"#probability that someone was a liar or detected as one by the polygraph
#P(liar) + P(truth | positive test )
paste("probability that someone was a liar or detected as one by the polygraph is",p_liar +((1 - p_spec)*p_truth))## [1] "probability that someone was a liar or detected as one by the polygraph is 0.28"