35. If a fair die is tossed twice, the probability that the first toss will be a number less than 4 and the second toss will be greater than 4 is

• 1/6

36. A class consists of 490 female and 510 male students. The students are divided according to their marks

	Passed	Did not pass
Female	430	60
Male	410	100

If one person is selected randomly, the probability that it did not pass given that it is female is:

• 0.12

37. Marks on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximately what percentage of the students have scores below 50?

• 11%

38. Suppose the test scores of 600 students are normally distributed with a mean of 76 and standard deviation of 8. The number of students scoring between 70 and 82 is:

• 328

39. The distribution of weights in a large group is approximately normally distributed. The mean is 80 kg. and approximately 68% of the weights are between 70 and 90 kg. The standard deviation of the distribution of weights is equal to:

• 10

40. The probability density function of a continuous random variable X is

. Find .

• 0.5625

41. Let X be a continuous random variable with density function Calculate the expected value ofX.

• 28/15

42. The probability density function of a continuous random variable X is . Find the value of k.

• 0.375

43. A continuous random variable X is uniformly distributed over the interval [10, 16]. The expected value of X is

• 13

44. If X and y are independent random variables with ,,and,,,. Thenis

• 0.56

45. How many different three-member teams can be formed from six students?

• 20

46. How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?

• 720

47. If p(e) is the probability that an event will occur, which of the followings must be false?

• P(E)= -1

48. A die is rolled. What is the probability that the number rolled is greater than 2 and even?

• 1/3

49. A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?

• 29/36

50. The cumulative distribution function for continuous random variable X is given by . Find the standard deviation.

• 

51. A continuous random variable X uniformly distributed on [-2;6]. Find E[X] and Var(X).

• 2 and

52. A continuous random variable X is exponentially distributed with the density . What is the E[X] and Var(X)?

• and

53. The expression is equivalent to

• 

54. Evaluate 1!+2!+3!

• 9

55. A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?

• 29/36

56. Your state issues license plates consisting of letters and numbers. There are 26 letters and the letters may be repeated. There are 10 digits and the digits may be repeated. How many possible license plates can be issued with two letters followed by three numbers?

• 676000

57. A random variable X has the cumulative distribution function

Compute the expectation of X.

• 5/6

58. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss?

• 1/2

59. A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?

• 9

60. A random variable Y has the following distribution:

Y | -1 0 1 2

P(Y)| 3C 2C 0.4 0.1 The value of the constant C is:

• 0.1

61. A random variable X has a probability distribution as follows:

X | 0 1 2 3

P(X) | 2k 3k 13k 2k

Then the probability that P(X < 2.0) is equal to

• 0.25

62. Which one of these variables is a continuous random variable?

• The time it takes a randomly selected student to complete an exam.

63. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall?

• 0.25

64. The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the "expected value" of the number of patients who are successfully treated?

• 32

65. A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured?

• 0.04

66. A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ...

• Probability distribution

67. Given a normal distribution with µ=100 and σ=10, what is the probability that X>75?

• 0.99

68. Which of the following is not a property of a binomial experiment?

• the probabilities of the two outcomes can change from one trial to the next

69. Which of the following random variables would you expect to be discrete?

• The number of children at a birthday party

70. Two events each have probability 0.2 of occurring and are independent. The probability that neither occur is

• 0.64

71. A smoke-detector system consists of two parts A and B. If smoke occurs then the item A detects it with probability 0.95, the item B detects it with probability 0.98 whereas both of them detect it with probability 0.94. What is the probability that the smoke will not be detected?

• 0.01

72. A class consists of 490 female and 510 male students. The students are divided according to their marks Passed and Did not pass

	Passed	Did not pass
Female	430	60
Male	410	100