12.3 Probability

Definition – Probability When you toss a coin, there are only two possible outcomes – heads or tails. A desired outcome is called SUCCESS. Any other outcome is called FAILURE. If an event can succeed in s ways and fail in f ways, then the probability of success, P(S), and of failure, P(F), are as follows:

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 1 When two coins are tossed, what is the probability that both are tails? Define success as HH and failure as all other options.

Example 2 – Probability with Combinations Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap?

Example 2 – Probability with Combinations Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap? Step 1: Determine how many 6-CD selections meet this condition.

Example 2 – Probability with Combinations Suppose you have 32 CDs – 18 Rock and 14 rap. Suppose that you randomly select 6 CDs to take on a trip. What is the probability that you select 3 Rock and 3 rap? Step 1: Determine how many 6-CD selections meet this condition.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes. Step 3: Find the total number, s+f, of possible 6-CD selection.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes. Step 3: Find the total number, s+f, of possible 6-CD selection.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes. Step 3: Find the total number, s+f, of possible 6-CD selection.

Example 2 Step 2: Use Fundamental Counting Principal (FCP) to find the number of successes. Step 3: Find the total number, s+f, of possible 6-CD selection.

Example 2 Step 4: Determine the probability.

Example 2 Step 4: Determine the probability.

Example 2 Step 4: Determine the probability.

Example 2 Step 4: Determine the probability.

Example 2 Step 4: Determine the probability. The probability that you randomly select 3 Rock and 3 Rap CDs is 0.3278.

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Calculator, How to [Math] button, then over to the PRB menu Option 3 will compute the number of combinations for you “nCr”

Example 2 Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

Example 2 Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

Example 2 Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

Example 2 Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

Example 2 Suppose that you have 4 dogs and 5 cats. What is the probability that you randomly select 2 dogs and 1 cat?

Assignment