Introductory Statistics

Lesson 3.2 A

Objective: SSBAT find conditional probability.

Standards: M11.E.3.1.1

Conditional Probability

The probability of an event occurring, given that another event has already occurred.

Notation:

P(B│A) means Probability of event B occurring given event A has occurred

P(A│B) means Probability of event A occurring given event B has occurred

Examples.

1. Two cards are selected in sequence from a deck of cards. Find the probability that he second card is a queen, given that the first card is a king. The king is not replaced.

Since the first card was a King and it was not replaced, there are now just 51 cards remaining, with 4 queens.

P(Q│K) = or 0.078

2. Two cards are chosen in sequence from a deck of cards. Find the probability that the second card is a heart, given the first card was the 10 of hearts. The first card is not replaced.

After the first card is chosen, there are just 51 cards remaining. The first card was also a heart, so now there are just 12 hearts.

P(Heart│10 of Hearts) = or 0.235

3. The table shows the results of a study in which researchers examined a child’s IQ and the presence of a specific gene in the child. Find the probability that a child has a high IQ, given that the child has the gene.

Find the Probability that a child has a high IQ, given that the child has the gene.

Since we know the child has the gene, we can just look at this column. There are 72 total children in this category.

Using just this category, find the Probability of High IQ.

P(High IQ │Gene Present) = = or 0.458

Gene Present

Gene not present

Total

High IQ 33 19 52

Normal IQ

39 11 50

Total 72 30 102

4. Use the same table to find the Probability that a child does not have the gene, given that the child has a normal IQ.

Gene Present

Gene not present

Total

High IQ 33 19 52

Normal IQ

39 11 50

Total 72 30 102

We are given the child has a Normal IQ, so therefore we will just use this data (row).

There are a total of 50 children who have a normal IQ.

P(No Gene│Normal IQ) = or 0.22

Independent Events

Two events are Independent if the occurrence of one of the events does NOT affect the probability of the other event.

Example - Rolling a Die and Tossing a Coin

What you roll on the die does not affect what you toss on the coin.

If events are not independent they are Dependent

Examples: Determine if the events are Independent or Dependent

1. Selecting a King from a deck of cards, not replacing it, and then selecting a Queen from the deck.

Dependent (not replacing the king changes the probability of selecting a queen)

2. Tossing a coin and getting a head, and then rolling a die and getting a 6.

Independent (what you get on the coin does not affect what you get on the die)

3. Driving 80 miles per hour and then getting a speeding ticket.

Dependent

4. Smoking a pack of cigarettes per day and developing emphysema (a lung disease)

Dependent

5. Exercising frequently and having a 4.0 grade point average

Independent

Complete worksheet 3.2 A