11 What odds should a person give in favor of the following events?

(a) A card chosen at random from a 52-card deck is an ace.

ace <- 4
total_cards <- 52

ace/total_cards
## [1] 0.07692308

\[P(Ace) = 4/52 = 7.6%\]

(b) Two heads will turn up when a coin is tossed twice.

Assuming each toss is independent from the other:

\[P(H) = 1/2\] \[P(HH) = 1/2 * 1/2 = 0.25% or 1 in 4\]

(1/2) * (1/2)
## [1] 0.25

(c) Boxcars (two sixes) will turn up when two dice are rolled.

\[P(6) = 1/6\] \[P(2x 6) = 1/6 * 1/6 = 2.77% = 1 in 36 chance\]

(1/6) * (1/6)
## [1] 0.02777778