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Solution

(a) What is the probability distribution for T?

(b) Find P(T>3)

rolldice <- 1/6

# n = 3 - 1
n <- 2

T3 <- pgeom(n, rolldice, lower.tail = F)

T3
## [1] 0.5787037

(c) Find P(T>6|T>3)

# n = 6 - 1
n2 <- 5

T6 <- pgeom(n2, rolldice, lower.tail = F)

new_T <- T3 * T6/T3

new_T
## [1] 0.334898