Example The probability that a horse will win a race is 2/7. Find the odds against the horse winning the race.
Solution P(lose) = 1 – 2/7 P(lose) = 5/7 Odds against = Odds against = 5:2
Payoff odds Payoff odds against event A = amount of net profit : amount bet
Example The odds against a horse winning is 5:2. You bet $15 on the horse. What is your net profit, if the horse wins?
Solution 5 : 2 = net profit : 15 Write: 2x = 75 X = $37.50 Get back $52.50 ($37.50 + $15)
Addition Rule for 2 events P(A or B) means P(event A happens OR event B happens OR they both happen) P(A or B) = P(A) + P(B) – P(A and B)
Example A card is drawn from a deck of 52 cards. What is the probability that it is either a King or a Heart?
Solution There are 4 Kings. There are 13 Hearts. There is 1 King of Hearts.
Solution There are 4 Kings. There are 13 Hearts. There is 1 King of Hearts. P(King or Heart) = 4/52 + 13/52 – 1/52 P(King or Heart) = 16/52 P(King or Heart) = 0.308
Example A card is drawn from a deck of 52 cards. What is the probability it is a King or a Queen?
Solution There are 4 Kings. There are 4 Queens. A card can not be a King and a Queen.
Solution There are 4 Kings. There are 4 Queens. A card can not be a King and a Queen. P(King or Queen) = 4/52 + 4/52 – 0/52 P(King or Queen) = 8/52 P(King or Queen) = 0.154
Mutually Exclusive Two events are mutually exclusive if they can not both occur at the same time. P(A and B) = 0 In the example, getting a King AND a Queen are mutually exclusive.
Tables to present data A sample of 1000 people was obtained. There were 500 men and 500 women. Of the men, 63 were left handed. Of the women, 50 were left handed. MenWomenTotal Left handed6350113 Right handed437450887 Total500 1000
Questions: If a person is randomly selected, what is the probability that: a. The person is a man b. The person is left handed c. The person is a left handed man d. The person is a man or is left handed
Solution The person is a man P(man) = 500/1000 P(man) = 0.500 The person is left handed P(left handed) = 113/1000 P(left handed) = 0.113
Solution The person is a left handed man P(left handed and man) = 63/1000 P(left handed and man) = 0.063 The person is a man or is left handed P(man or left handed) =.500 +.113 -.063 P(man or left handed) = 0.550
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