A bag contains 5 green and 7 red jellybeans. How many ways
can 5 jellybeans be withdrawn from the bag so that the number of green
ones withdrawn will be less than 2?
## combination of choosing 0 green
zero <- choose(7,5)
## combination of choosing 1 green
one <- choose(5,1) * choose(7,4)
both <- zero + one
both
## [1] 196
If a coin is tossed 5 times, and then a standard six-sided
die is rolled 2 times, and finally a group of three cards are drawn from
a standard deck of 52 cards without replacement, how many different
outcomes are possible?
coin <- 2^5
deck <- 6^2
card <- 52 * 51 * 50
coin * deck * card
## [1] 152755200
3 cards are drawn from a standard deck without replacement.
What is the probability that at least one of the cards drawn is a 3?
Express your answer as a fraction or a decimal number rounded to four
decimal places.
prob <- 1-((48/52) * (47/51) * (46/50))
round(prob, digits = 4)
## [1] 0.2174
Lorenzo is picking out some movies to rent, and he is
primarily interested in documentaries and mysteries. He has narrowed
down his selections to 17 documentaries and 14 mysteries.
print(choose(31,5))
## [1] 169911
In choosing what music to play at a charity fund raising
event, Cory needs to have an equal number of symphonies from Brahms,
Haydn, and Mendelssohn. If he is setting up a schedule of the 9
symphonies to be played, and he has 4 Brahms, 104 Haydn, and 17
Mendelssohn symphonies from which to choose, how many different
schedules are possible? Express your answer in scientific notation
rounding to the hundredths place
symph <- choose(4,3) * choose(104,3) * choose(17,3) * factorial(9)
signif(symph, digits = 4)
## [1] 1.797e+14
An English teacher needs to pick 13 books to put on his
reading list for the next school year, and he needs to plan the order in
which they should be read. He has narrowed down his choices to 6 novels,
6 plays, 7 poetry books, and 5 nonfiction books. Step 1. If he wants to
include no more than 4 nonfiction books, how many different reading
schedules are possible? Express your answer in scientific notation
rounding to the hundredths place.
book<- choose(24,13) +
choose(25,12) * choose(5,1) +
choose(24,11) * choose(5,2) +
choose(24,10) * choose(5,3) +
choose(25,9) * choose(5,4)
signif(book * factorial(13), digits = 4)
## [1] 5.186e+17
Step 2. If he wants to include all 6 plays, how many
different reading schedules are possible? Express your answer in
scientific notation rounding to the hundredths place.
signif(choose(6,6) * choose((24 - 6),7) * factorial(13), digits = 4)
## [1] 1.982e+14
Zane is planting trees along his driveway, and he has 5
sycamores and 5 cypress trees to plant in one row. What is the
probability that he randomly plants the trees so that all 5 sycamores
are next to each other and all 5 cypress trees are next to each other?
Express your answer as a fraction or a decimal number rounded to four
decimal places.
way <-2
trees <- 10
syc <-5
cyp <- 5
ans <- round(way/(factorial(trees)/(factorial(syc)^2)),4)
ans
## [1] 0.0079
If you draw a queen or lower from a standard deck of cards,
I will pay you $4. If not, you pay me $16. (Aces are considered the
highest card in the deck.) Step 1. Find the expected value of the
proposition. Round your answer to two decimal places. Losses must be
expressed as negative values.
probability_win <- 11/13
probability_loss <- 1 - probability_win
payoff_win <- 4
payoff_loss <- -16
expected_value <- (probability_win * payoff_win) + (probability_loss * payoff_loss)
expected_value <- round(expected_value, 2)
expected_value
## [1] 0.92
. If you played this game 833 times how much would you
expect to win or lose? Round your answer to two decimal places. Losses
must be expressed as negative values.
num_games <- 833
total_expected_value <- expected_value * num_games
total_expected_value <- round(total_expected_value, 2)
total_expected_value
## [1] 766.36
expected_value <- ((44/52) * 4) + ((8/52) * -16)
round(expected_value, digits = 2)
## [1] 0.92
round(expected_value * 833, digits = 2)
## [1] 768.92