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This quiz contains multiple-choice problems on the addition and multiplication theorem on probability, probability distribution, Bayes’ theorem, generating functions, inclusion and exclusion principles, logarithmic and power series.
A ball is thrown at a circular bin such that it will land randomly over the area of the bin. What is its probability of landing closer to the centre than to the edge?
51%
25%
72%
34%
A programmer has a 95% chance of finding a bug every time she compiles her code, for which she takes three hours to rewrite. Find the probability of her finishing the program by the end of the workday (assuming that a workday is 9 hours).
76%
44%
37%
28%
A football player has a 45% chance of getting a hit on any given pitch. What is the probability that the player earns a hit ignoring the balls before he strikes out (that requires four strikes)?
0.36
0.95
0.67
0.59
What is the variance of a geometric distribution having parameter p = 0.72?
54%
76%
13%
69%
The probability of rain for tomorrow is 0.72. Find the probability that it does not rain tomorrow.
65%
43%
28%
32%
Suppose a rectangle’s edges equals i = 4.7 and j = 8.3. In adjacent rectangle edges, a straight line is drawn through two randomly selected points, K and L. Find the probability condition such that the area of the drawn triangle is smaller than c = 9.38.
K - L ≤ 18.76
K + L ≤ 18.76
K * L ≤ 18.76
K / L ≤ 18.76
What’s the number of bacteria per field if 2350 bacteria are randomly distributed over 340 fields (all fields are of the same size) next to each other?
4.98
3.875
6.91
7.37
What is the possibility of the inequality x2 + b > ax being true, given a = 32.4, b = 76.5 and x ∈ [0,30]?
1.91
4.3
2.94
6.1
A bucket holds five purple, 15 grey and 25 green balls. Find the probability that a randomly picked ball is neither grey nor purple.
5/9
12/13
51/43
2/7
A personal computer has a length of time between battery charges, normally distributed with a mean of 66 hours and a standard deviation of 20 hours. What is the probability that the length of time will be between 58 and 75 hours?
0.595
3.44
0.0443
1.98
The lifespan of an instrument produced by a machine has a normal distribution with a mean of 9.4 months and a standard deviation of 3.2 months. What is the probability that an instrument made by this machine will last between 6 and 11.6 months?
0.642
0.4098
0.16
0.326
The speeds of several bicycles have a normal distribution model with a mean of 83 km/hr and a standard deviation of 9.4 km/hr. What is the probability of a randomly picked bicycle travelling more than 95 km/hr?
0.1587
0.38
0.49
0/278
The length of similar metals produced by a hardware store is approximated by a normal distribution model having a mean of 7 cm and a standard deviation of 0.35 cm. What is the probability that the length of a randomly chosen metal is between 5.36 and 6.14 cm?
0.562
0.2029
3.765
1.576
Let us say that X is a normally distributed variable with a mean (μ) of 43 and a standard deviation (σ) of 6.4. Determine the probability of X < 32.
0.341
0.962
6.231
0.44
Suppose R is a random real number between 5 and 9. What is the probability that R is closer to 5 than 6?
12.5%
18%
73%
39.8%
