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## combn## ## Rmetrics Package fBasics## Analysing Markets and calculating Basic Statistics## Copyright (C) 2005-2014 Rmetrics Association Zurich## Educational Software for Financial Engineering and Computational Science## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.## https://www.rmetrics.org --- Mail to: info@rmetrics.org## ## Rmetrics Package fOptions## Pricing and Evaluating Basic Options## Copyright (C) 2005-2014 Rmetrics Association Zurich## Educational Software for Financial Engineering and Computational Science## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.## https://www.rmetrics.org --- Mail to: info@rmetrics.org##
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## erf## prob
## TRUE11. What odds should a person give in favor of the following events?
- A card chosen at random from a 52-card deck is an ace.
In R
(Aces <- sum(cards()$rank == "A"))
## [1] 4
(ncards <- nrow(cards()))
## [1] 52
Aces/ncards
## [1] 0.07692308P(A) = 4/52 = 1/13 Therefore, the odds are 1:12
- Two heads will turn up when a coin is tossed twice.
In R
(samp_space <- tosscoin(2))
## toss1 toss2
## 1 H H
## 2 T H
## 3 H T
## 4 T T
(Nsamp_space <- nrow(samp_space))
## [1] 4
(desired_outcome <- nrow(subset(samp_space, toss1 == "H" & toss2 == "H")))
## [1] 1
desired_outcome/Nsamp_space
## [1] 0.25P(A) = 1/4
Therefore, the odds are 1:3.
- Boxcars (two sixes) will turn up when two dice are rolled
(samp_space <- rolldie(2))
## X1 X2
## 1 1 1
## 2 2 1
## 3 3 1
## 4 4 1
## 5 5 1
## 6 6 1
## 7 1 2
## 8 2 2
## 9 3 2
## 10 4 2
## 11 5 2
## 12 6 2
## 13 1 3
## 14 2 3
## 15 3 3
## 16 4 3
## 17 5 3
## 18 6 3
## 19 1 4
## 20 2 4
## 21 3 4
## 22 4 4
## 23 5 4
## 24 6 4
## 25 1 5
## 26 2 5
## 27 3 5
## 28 4 5
## 29 5 5
## 30 6 5
## 31 1 6
## 32 2 6
## 33 3 6
## 34 4 6
## 35 5 6
## 36 6 6
(Nsamp_space <- nrow(samp_space))
## [1] 36
(desired_outcome <- nrow(subset(samp_space, X1 == 6 & X2 == 6)))
## [1] 1
desired_outcome/Nsamp_space
## [1] 0.02777778P(A) = 1/36 Therefore, the odds are 1:35.