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 theTotal: 2-7, you loseTotal : 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) = 452

P(second ace first ace)

= 351

3 because an Ace is already gone

P(2A) = P(first ace) X P(second ace first ace)

= 452

X 351

= 122652

= 1221

Product rule for dependent events

P(A and B) = P(A) X P(B I A)

• Pg 334

• 1-4,6,7,10