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SINGLE-EVENT PROBABILITY
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Single-event probability is the probability of a single event occurring within a given set of possible outcomes If you were to apply this to the probability of obtaining heads in a coin ip, there is one successful outcome (heads) and two possible outcomes (heads or tails) So the probability of obtaining heads in a coin ip is: p= s 1 = n 2
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Since the probability is a fraction, it can be expressed as a percentage, with the probability of obtaining heads in a coin ip being 50 percent Single-event probability can also be applied to a single playing card drawn from a standard deck of 52 cards To determine the probability that a selected card is of a black suit, you rst note that a card can be selected from a deck in n = 52 different ways Since there are two black suits (clubs and spades) with 13 cards per suit, a card of a black suit can be drawn from the deck in s = 26 different ways Thus, the probability that the selected card is a card of a black suit is: p= s 26 1 = = n 52 2
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CHAP 14: PROBABILITY AND STATISTICS
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EXAMPLE: What is the probability of not selecting the king of hearts from a deck
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of cards SOLUTION: To determine the probability of not selecting the king of hearts, let s determine the probability of selecting the king of hearts Since the king of hearts is but 1 s Thus, one of 52 cards, the probability of selecting the king of hearts is p = = n 52 the probability, q, of not selecting the king of hearts is q = 1 p = 52 1 = 51 52 52 52
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MULTIPLE-EVENT PROBABILITY
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In single-event probability, you seek to determine the probability or likelihood of a single successful outcome out of a set of possible outcomes In multiple-event probability, you seek to determine the probability or likelihood of two or more successful outcomes occurring, but not at the same time (referred to as mutually exclusive events) or the probability of one outcome occurring and another outcome not occurring (referred to as independent events)
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Probability Involving Mutually Exclusive Events
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Let us say that the probability of one successful event is P(A), the probability of another is P(B), and the two events have no common outcomes Then the probability that either of these events occurring P(A or B) is the sum of their individual probabilities, P(A) + P(B) or P(A or B) = P(A) + P(B)
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EXAMPLE: Upon rolling a pair of dice, what is the probability that the sum of the
two numbers on the dice is either 6 or 12 SOLUTION: The number of total possible outcomes from the roll of two dice is 36 In other words, there are 36 different pairs of numbers that can be obtained You rst need to determine the number of possible outcomes yielding a sum of 6
PART VI: REVIEWING PCAT MATH SKILLS
and 12 from the two dice The number of possible outcomes yielding a sum of 6 is 5 or {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)} The probability of yielding a sum of 6 between the two dice is P(A) = P(6) = 5 36
The number of possible outcomes yielding a sum of 12 is 1 or {(6, 6)} The probability of yielding a sum of 12 between the two dice is P(B) = P(12) = 1 36
Upon the roll of two dice, you cannot obtain a sum of 6 and a sum of 12 at the same time; the two successful outcomes thus are mutually exclusive The probability that the sum of the two dice is either 6 or 12 is: P(A or B) = P(A) + P(B) = P(6) + P(12) = 5 1 6 1 + = = 36 36 36 6