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EXAMPLE 1

Let event A be selecting a 10 and event B be selecting a face card. A has 4 outcomes and B has 12 outcomes. Because A and B are disjoint, the probability is:. 4. 4. 16. 12. 0.308. =. =. +. =. 13. 52. 52. 52. EXAMPLE 1. Find probability of disjoint events.

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EXAMPLE 1

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  1. Let event Abe selecting a 10 and event Bbe selecting a face card. Ahas 4 outcomes and Bhas 12 outcomes. Because Aand Bare disjoint, the probability is: 4 4 16 12 0.308 = = + = 13 52 52 52 EXAMPLE 1 Find probability of disjoint events A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10or a face card? SOLUTION P(A orB) = P(A)+ P(B)

  2. SOLUTION Let event Abe selecting a face card and event Bbe selecting a spade. Ahas 12 outcomes and Bhas 13 outcomes. Of these, 3 outcomes are common to Aand B. So, the probability of selecting a face card or a spade is: EXAMPLE 2 Standardized Test Practice

  3. = P(A)+ P(B)– P(AandB) P(A orB) 12 13 3 – = + 52 52 52 22 = 52 11 = 26 ANSWER The correct answer is B. EXAMPLE 2 Standardized Test Practice

  4. Senior Class Out of 200 students in a senior class, 113 students are either varsity athletes or on the honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll? EXAMPLE 3 Use a formula to find P(A and B) SOLUTION Let event Abe selecting a senior who is a varsity athlete and event Bbe selecting a senior on the honor roll. From the given information you know that:

  5. 113 51 74 P(A) ,P(B) , andP(A orB) = = = 200 200 200 P(A orB) = P(A)+P(B)–P(A andB) 74 51 113 –P(A andB) + = 200 200 200 74 51 113 P(A andB) – + = 200 200 200 12 3 P(A andB) = = = 0.06 200 50 EXAMPLE 3 Use a formula to find P(A and B) FindP( A and B ) Write general formula. Substitute known probabilities. Solve for P(Aand B). Simplify.

  6. Selecting an ace or an eight 2 13 ANSWER for Examples 1, 2, and 3 GUIDED PRACTICE A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event.

  7. A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event. Selecting a 10or a diamond 0.308 ANSWER for Examples 1, 2, and 3 GUIDED PRACTICE

  8. ANSWER 0.095 P(A andB) = What If? In Example 3, suppose 32 seniors are in the band and 64 seniors are in the band or on the honor roll. What is the probability that a randomly selected senior is both in the band and on the honor roll? for Examples 1, 2, and 3 GUIDED PRACTICE

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