1. AND probability AND probability for two events Chapter 10.5 A

2. Two events, A and B, are called independent if the outcome of one has no effect on the outcome of the other.

3. P(> $500 AND bankrupt) = P(>$500) ∙ P(bankrupt) P(> $500 AND bankrupt) =

4. P(1 st woman AND 2 nd woman AND man) = P(1 st woman) ∙ P(2 nd woman) ∙ P(man)

5. Two events, A and B, are called dependent if the outcome of one affects the outcome of the other. You randomly select two cards from a standard deck of cards. Find the probability that the first one is a spade and the second one a black card if you do not replace the first card. The probability that B will occur given that A already happened is called the conditional probability of B given A and shown as P(B|A).

6. You randomly select two cards from a standard deck of cards. Find the probability that the first one is a spade and the second one a black card if you do not replace the first card. P(spade AND black) = P(spade) ∙ P(black|spade) P(spade AND black) = With replacement: independent events: P(spade AND black) = P(spade) ∙ P(black) P(spade AND black) =

7. P(A AND B) = P(A) ∙ P(B|A) In conclusion: The probability of two consecutive events is given by: If the events are independent, then P(B|A) = P(B), in other words, event A has no effect on event B. If the events are dependent, then P(B|A) ≠ P(B), in other words, event A affects the output for event B, and P(B|A) must be carefully computed.

8. For practice: P (1 st parent AND 2 nd parent AND 3 rd parent ) = = P(parent reads) · P(parent reads) · P(parent reads) = = (.046) · (0.46) · (0.46) = 0.0973 = 9.73%

9. A gumball machine contains 75 blue balls, 90 red balls, 15 white balls, and 25 green balls. You buy two gumballs. a)Find the probability that the first gumball is red and the second one blue. b)Find the probability that both gumballs are white. For practice: P (1 st red AND 2 nd blue) = = P(red) · P(blue│red) = (90/205) · (75/204) = 0.1614 = 16.14% P (both white) = P (1 st white AND 2 nd white) = = P(white) · P(white│white) = (15/205) · (14/204) = 0.0050 = 0.5%

10. Patty Patriot has been slacking in her classes as of lately and her grades have slipped a bit. She knows that the probability of her getting an A in Advanced Algebra is now only 16%. For her Chemistry class, Patty’s probability of getting an A is higher, a 23%. a)What is the probability of Patty getting an A in both classes, Advanced Algebra and Chemistry? b)What is the probability of Patty getting an A in either class? c)What is the probability of Patty not getting an A in Advanced Algebra? d)What is Patty’s probability of not getting an A in either class? P (Alg AND Chem) = P(Alg) · P(Chem) = 0.0368 = 3.68% P (Alg OR Chem) = P(Alg) + P(Chem) − P(Alg) · P(Chem) = 0.3532 = 35.32% P (NOT Alg) = 1 − P(Alg) = 0.84 = 84% P (NOT Alg AND NOT Chem) = P(NOT Alg) · P(NOT Chem) = =(0.84) · (0.77) = 0.6468 = 64.68% For practice:

11. P (NOT Alg AND NOT Chem) = 1 − P(Alg OR Chem) = =1 − 0.3532 = 0.6468 = 64.68% d) What is Patty’s probability of not getting an A in either class? P (NOT Alg AND NOT Chem) = P(NOT Alg) · P(NOT Chem) = =(0.84) · (0.77) = 0.6468 = 64.68% Another method for the same problem: