Essay About Theme of the Tide Rises and the Tide Fall

406 WordsJan 28, 20152 Pages
EXAMPLE 3 Finding Probability with Permutations or Combinations Each student received a 4-digit code to use the library computers, with no digit repeated. Manu received the code 7654. What was the probability that he would receive a code of consecutive numbers? Step 1 Determine whether the code is a permutation or a combination. Order is important, so it is a permutation. Step 2 Find the number of outcomes in the sample space. The sample space is the number of permutations of 4 of 10 digits. 10! ___ = _ = 10 · 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 = 5040 6·5·4·3·2·1 6! Step 3 Find the favorable outcomes. The favorable outcomes are the codes 0123, 1234, 2345, 3456, 4567, 5678, 6789, and the reverse of each of these numbers. There are 14 favorable outcomes. 10P 4 Step 4 Find the probability. 14 1 P (consecutive numbers) = _ = _ 5040 360 The probability that Manu would receive a code of consecutive numbers 1 was ___. 360 3. A DJ randomly selects 2 of 8 ads to play before her show. Two of the ads are by a local retailer. What is the probability that she will play both of the retailer’s ads before her show? Geometric probability is a form of theoretical probability determined by a ratio of lengths, areas, or volumes. EXAMPLE 4 Finding Geometric Probability Three semicircles with diameters 2, 4, and 6 cm are arranged as shown in the figure. If a point inside the figure is chosen at random, what is the probability that the point is inside the shaded region? Find the ratio of the area of the shaded region to the area of the entire semicircle. The area of a 1 semicircle is __πr 2. 2 First, find the area of the entire semicircle. 1 A t = _π(3 2) = 4.5π Total area of largest semicircle 2 Next, find the unshaded area. ⎡1 ⎤ ⎡1 ⎤ A u = ⎢ _π(2 2) ⎥ + ⎢ _π(1 2) ⎥ = 2π + 0.5π = 2.5π Sum of areas of ⎣2 ⎦ ⎣2 ⎦ Subtract to find the shaded area. A s = 4.5π - 2.5π = 2π As

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