R Notebook

Hw1

Example 2.14

A fair coin is repeatedly tossed. Estimate the probability that you observe Heads for the third time on the 10th toss.

Answer

event <- replicate(10000, {
  coinToss <- sample(c("H", "T"), 10, replace = TRUE) # Simulate outcome of 10 coin tosses
  coinToss
  sum(coinToss == "H") # need 3 heads
  sum(coinToss == "H") == 3
  coinToss[1:9] # need only 2 heads in first 9 tosses to make sure 10th is heads
  sum(coinToss[1:9] == "H") == 2 # add up all heads
  sum(coinToss == "H") == 3 & sum(coinToss[1:9] == "H") == 2 # both events need to be true to have 10th coin be heads
})
mean(event)

[1] 0.0357