S: The number of items in the sample that are classified as successes. h(s; N, n, S): hypergeometric probability - the probability that an n-trial hypergeometric experiment results in exactly s successes, when the population consists of N items, S of which are classified as successes. A vase contains 12 red balls, 6 blue balls and two white balls. Draw six balls without replacing them, what is the chance of getting 4 red balls? Now the binomial distribution does not apply, because rule 1 is violated. If e.g. one starts by drawing a red ball (with probability 12/20), the chance of getting another one in the second draw is no longer 12/20 but 11/19.
4. standard six-sided dice are rolled. One die is blue and the other is red a. . Create a table to represent the sample space b. For each probability below, express the answer as a fraction, as a decimal, and as a percentage. i. What is the probability of rolling a sum greater than ten ii. What is the probability that the number on the red die is one larger than the number on blue dice? iii. What is the probability that the sum of the two numbers is less than 11? Table has a header with 1,2,3,4,5,6 across and the same numbers down. The boxes are filled with the sums. i. 3/36 = 1/12 ii. Six of the boxes have the two dice the same, e.g., 1,1 Red and blue are equally like to be larger on the remaining 30. (30/2)/36 = 5/12 iii. The opposite of i. 11/12 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. 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? Jack selects a book and it is a novel. There are 23 books remaining in the box. There are 16 books remaining that are not novels. Probability of NOT a novel is 16 out of 23. The answer will remain the same regardless of the first book chosen by Jack since there are 8 copies of each style book. 7. The probability that Prasha will score above a 90 on a mathematics test is . What is the probability that she will score above a 90 on exactly 3 of the 4 tests this quarter?
8. A company manufacturing laptops believes that 5% of their computers are faulty. They take a sample of 30 computers. Showing your calculations a. , find the probability thatTwo of the laptops are faulty. b. More than two of the laptops are faulty. p = probability the laptop is faulty. q = probability the laptop is not faulty. p = .05 q = 1 - .05 = .95 since this appears to be a binomial probsbility type problem, then the formula is: p(x) = c(n,x) * p^x * q^(n-x)
c(n,x) = n! / (x! * (n-x)!) n = 30 p = .05 q = .95 p(2) = c(30,2) * .05^2 * .95^28 = 435 * .0025 * .2378268853 = .2586367377.
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