Dependent and Independent Events

Events are said to be independent if the occurrence of one event has no effect on the occurrence of another. For example, Flipping a coin 5 times in a row represents a series of independent events. (The first flip has no effect on the second flip)

A coin is flipped and a die is rolled. What is the probability of flipping heads and rolling 5? A: flipping head, B: rolling a 5 P(A and B) = P(A) X P(B) = 1/2 X 1/6 = 1 / 12

The product rule for independent events P(A and B) = P(A) X P(B) Find the probability of tossing tails and rolling a 4. P(A) = 1/2 X 1/6 1/12

Conditional Probability

Consider a slot machine… Usually, you are asked how much you want to bet… $1, $5, or $10?

How much would you bet if you knew the first 3 results?... $1, $5, or $10?

Consider the game: Dice Total Roll a pair of dice, if the Total: 2-7, you lose Total : 8-12, you win Would you play? What if you knew the first roll was a 6? Would you play?

Conditional Probability involves calculations, given that a certain condition has been met. This occurs when events are dependent.

Consider a deck of cards. Find the probability of drawing 2 Aces, one after the other. A: drawing an ace, B: drawing an ace P(A and B) = P(A) X P(B given that A has occurred ) = P(A) X P(B A)

P(first ace) = 4 52 P(second ace first ace) = because an Ace is already gone

P(2A) = P(first ace) X P(second ace first ace) = 4 52 X 3 51 = = 1 221

Product rule for dependent events P(A and B) = P(A) X P(B I A)

Pg ,6,7,10