Scrabble

M <- 55
N <- 42

(choose(M, 7) + choose(M, 6) * choose(N, 1) + choose(N, 6) * choose(2, 1) + 
  choose(N, 7) + choose(N, 6) * choose(M, 1) + choose(N, 6) * choose(2, 1) +
  choose(N, 1) * choose(M, 5) + choose(2, 1) * choose(M, 5) +
  choose(M, 1) * choose(N, 5) + choose(2, 1) * choose(N, 5) +
  choose(N, 6) +
  choose(M, 6)) / choose(100, 7)

## [1] 0.1244888

Po vytvoreni slova ROŠT:

N <- 39
(choose(N, 4) + choose(N, 3))/choose(93, 4)

## [1] 0.03130079

Testovanie krvi

p <- seq(from = 0, to = 0.1, by = 0.001)
EX1 <- 1 * (1 - p)^50 + 51 * (1 - (1 - p)^50)
plot(p, EX1, type = "l")

p <- seq(from = 0, to = 0.01, by = 0.0001)
EX <- 1 * (1 - p)^50 + 51 * (1 - (1 - p)^50)
plot(p, EX, type = "l")

p <- 0.01
1 * (1 - p)^50 + 51 * (1 - (1 - p)^50)

## [1] 20.7497

p1 <- (1 - p)^50
p2 <- 2 * (1 - p)^25 * (1 - (1 - p)^25)
p3 <- 1 - p1 - p2
2 * p1 + 27 * p2 + 52 * p3

## [1] 13.10893