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

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

ace_card <- 4
total_cards <- 52

ace_card/total_cards
## [1] 0.07692308

\[ P(Ace)=4/52 = 0.076\]

1.2 Two heads will turn up when a coin is tossed twice.

Assuming each toss is independent from the other:

\[ P(H)=1/2 \\ P(HH)=1/2 * 1/2=0.25 \]

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

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

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

\[ P(6)=1/6 \\ P(2x6)=1/6 * 1/6= 0.0277 \]