Red die blue die 1 2 3 4 5 6 1 1 1 1 2 1 3 1 3 1 5 1

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Red die Blue die 1 2 3 4 5 6 1 1 , 1 1, 2 1, 3 1, 3 1, 5 1, 6 2 2 , 1 2 , 2 2 , 3 2 , 4 2 , 5 2 , 6 3 3 , 1 3 , 2 3 , 3 3 , 4 3 , 5 3 , 6 4 4 , 1 4 , 2 4 , 3 4 , 4 4 , 5 4 , 6 5 5 , 1 5 , 2 5 , 3 5 , 4 5 , 5 5 , 6 6 6 , 1 6 , 2 6 , 3 6 , 4 6 , 5 6 , 6 P (red 1 larger than blue) = 5/36 P (red 1 larger than blue) = 0.138 P (red 1 larger than blue) = 0.138 x 100 P (red 1 larger than blue) = 13.8%
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Therefore the probability of the number on the red die being one larger than the number on the blue die is 1/12 in a fraction, 0.138 in a decimal, or 13.8%. iii. What is the probability that the sum of the two numbers is less than 11? Red die Blue die 1 2 3 4 5 6 1 1 , 1 1, 2 1, 3 1, 3 1, 5 1, 6 2 2 , 1 2 , 2 2 , 3 2 , 4 2 , 5 2 , 6 3 3 , 1 3 , 2 3 , 3 3 , 4 3 , 5 3 , 6 4 4 , 1 4 , 2 4 , 3 4 , 4 4 , 5 4 , 6 5 5 , 1 5 , 2 5 , 3 5 , 4 5 , 5 5 , 6 6 6 , 1 6 , 2 6 , 3 6 , 4 6 , 5 6 , 6 P (sum <11) = 33/36 P (sum <11) = 11/12 P (sum <11) = 0.916 P (sum <11) = 0.916 x 100 P (sum <11) = 91.6% Therefore the probability that the sum of the two numbers is less than 11 is 11/12 in a fraction, 0.916 in a decimal, or 91.6%. 8 marks
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5. Use a tree diagram to explain why the probability that a family with four children all have the same gender is . Assume that the probability of having a girl is equal to the probability of having a boy. 6. In a library box, there are 8 novels, 8 biographies and 8 war history books. If Jack selects two books at random, what is the probability that the two books are of different types? There is a total of 24 books
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There are 3 ways to choose two different types of books: (novel + biography), (biography + war), (novel + war) Since there are 8 novels of each type and 3 ways to pick 2 different types, do the equation (8 x 8) x 3 = 192 To choose 2 from 24 books do the equation: 24C2 = 276 P (two different types) =192/276 P (two different types0 = 16/23 Therefore the probability of selecting 2 different types of books is 16/23 or 0.6957. 3 marks 7. The probability that Prasha will score above a 90 on a mathematics test is 4/5 (0.8). What is the probability that she will score above a 90 on exactly 3 of the 4 tests this quarter? P (3) = 4 C 3 x 0.8 (3) x (0.2) 1 P (3) = 256/625 P (3) = 0.4096 Therefore the probability that Prasha will score above 90 on exactly 3 of her 4 math tests this quarter is 0.4096. 4 marks 8. A company manufacturing laptops believes that 5% of their computers are faulty. They take a sample of 30 computers. Showing your calculations, find the probability that; a. Two of the laptops are faulty. P (2) = 30 C 2 x 0.05 2 x (1-0.05) 28 P (2) = 30 C 2 x 0.05 2 x 0.95) 28 P (2) = 0.2586 Therefore the probability that two of the laptops are faulty is 0.2586 b. More than two of the laptops are faulty. First, I need to calculate the probabilities of having 3-30 faulty laptops. I did this through excel as shown here:
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Next, I need to add the sums of the probability of having 3-30 faulty laptops. The sum of P (3-30) = 0.12705
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Therefore the probability of having more than two faulty laptops is 0.121705. 4 marks 9. There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals.
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  • Fall '19
  • Probability theory, Binomial distribution, Hypergeometric Distribution

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