DB Week 5

Exercise 11 page 36

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

• A card chosen at random from a 52 card deck is an ace
• Two Heads will turn up when a coin is tossed twice
• Boxcars (2 6’s) will turn up when two dice are rolled

Since we can find the probability of each event \(p(E)\) when can use \(p/(1 -p)\) to find \(r/s\) or r to s odds by definition 1.4 on page 28

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

prob_ace <-  1/13

prob_ace / (1 - prob_ace)

## [1] 0.08333333

The odds a card chosen at random from a 52 card deck is an ace is 1:12

Two Heads will turn up when a coin is tossed twice

p_twoheads <-  1/4

p_twoheads / (1 - p_twoheads)

## [1] 0.3333333

The odds two Heads will turn up when a coin is tossed twice is 1:3

Boxcars (2 6’s) will turn up when two dice are rolled

p_boxcars <-  1/36

p_boxcars / (1 - p_boxcars)

## [1] 0.02857143

The odds two Heads will turn up when a coin is tossed twice is 1:35