2-7 Probability of Compound Events

Independent Events – events that do not effect each other To calculate the probability of 2 independent events: Find the probability of each one, then multiply Ex. What is the probability of rolling a 1 and then rolling a 2 on a standard die. P (1) = P (2) = P (1 then 2) =

Replacement In some situations, there is the possibility of replacement. For example, when picking 2 cards from a deck, you can put the 1 st card back before you draw the 2 nd card. This is replacement. When calculating probabilities for these types of situations, you must consider whether or not the item is being replaced.

Ex. What is the probability of picking 1 ace and 1 king from a deck of cards. Note: There are 52 cards in a standard deck, with 4 aces and 4 kings. With replacement P (one ace) = P (one king) = Without replacement P (one ace) = P (one king) =

Dependent events influence each other. To calculate the probability of 2 dependent events: Find the probability of each one, then multiply. The calculation isn’t really different…what changes is the probability of the 2 nd event.

Let’s try some: 1.Suppose you roll a red die and a blue die. What is the probability that you will roll a 5 on the red and a 1 or 2 on the blue. 2.There is a bag of marbles. There are 4 white, 3 black, 2 purple, 2 red, and 4 green. Find the probability of choosing a purple, then a red after replacing the 1 st marble. 3.Same bag of marbles. Find the probability of choosing a black then a red, without replacing the 1 st marble.