Home › Board exam reviewer › Probability and statistics

Probability and statistics: board exam questions with solutions

On the ECE exam under Mathematics and the REE exam under Mathematics. Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

Loading the reviewer… (it needs JavaScript)

Questions

1. What is the arithmetic mean of 4, 8, 6, 10 and 12?

  1. 6
  2. 8
  3. 10
  4. 40
Show the answer and solution

Answer: B. 8

(4 + 8 + 6 + 10 + 12)/5 = 40/5 = 8.

2. Two fair dice are rolled. What is the probability that the sum is 7?

  1. 1/12
  2. 1/6
  3. 7/36
  4. 1/36
Show the answer and solution

Answer: B. 1/6

Six of the 36 outcomes give a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). 6/36 = 1/6.

3. Find the population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9.

  1. 2.14
  2. 4
  3. 2
  4. 5
Show the answer and solution

Answer: C. 2

The mean is 5 and the squared deviations sum to 32. σ² = 32/8 = 4, so σ = 2. Dividing by n − 1 gives the sample value, 2.14.

4. A production line makes 5% defective diodes. In a random sample of 10, what is the probability of exactly one defective?

  1. 0.0500
  2. 0.5987
  3. 0.0315
  4. 0.3151
Show the answer and solution

Answer: D. 0.3151

By the binomial formula, P = C(10,1)(0.05)(0.95)⁹ = 10 × 0.05 × 0.6302 = 0.3151.

5. A and B are independent events with P(A) = 0.4 and P(B) = 0.5. Find P(A or B).

  1. 0.9
  2. 0.2
  3. 0.45
  4. 0.7
Show the answer and solution

Answer: D. 0.7

P(A ∪ B) = P(A) + P(B) − P(A)P(B) = 0.4 + 0.5 − 0.2 = 0.7.

6. In how many ways can a 3-member committee be chosen from 8 engineers?

  1. 56
  2. 336
  3. 24
  4. 512
Show the answer and solution

Answer: A. 56

Order does not matter, so C(8,3) = 8!/(3!5!) = 56. 336 is the number of ordered arrangements, P(8,3).

7. Supplier A provides 60% of a plant's capacitors, of which 2% are defective. Supplier B provides the rest, of which 5% are defective. A capacitor picked at random is defective. What is the probability that it came from B?

  1. 0.400
  2. 0.020
  3. 0.625
  4. 0.375
Show the answer and solution

Answer: C. 0.625

P(defective) = 0.6(0.02) + 0.4(0.05) = 0.012 + 0.020 = 0.032. By Bayes' theorem, P(B | defective) = 0.020/0.032 = 0.625.

8. Resistor values are normally distributed with mean 100 Ω and standard deviation 2 Ω. About what percentage lie between 98 Ω and 102 Ω?

  1. 68.27%
  2. 95.45%
  3. 34.13%
  4. 99.73%
Show the answer and solution

Answer: A. 68.27%

98 to 102 Ω is μ ± 1σ, which covers about 68.27% of a normal distribution.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. Each of 8 independent components fails with probability 0.1. What is the probability that exactly 4 fail?

  1. 0.00459
  2. 0.0000656
  3. 0.05
  4. 0.007
Show the answer and solution

Answer: A. 0.00459

Binomial: C(8,4)·0.1^4·0.9^4 = 70 × … = 0.00459.

10. Find the population standard deviation of 4, 13, 5, 19, 5.

  1. 6.57
  2. 1.84
  3. 5.88
  4. 34.6
Show the answer and solution

Answer: C. 5.88

Mean 9.2; population SD = √(Σ(x − x̄)²/N) = 5.88 (dividing by N − 1 gives the sample SD 6.57).

Other topics in the same subjects

Algebra · Trigonometry · Analytic geometry · Differential calculus · Integral calculus · Differential equations · Complex numbers · Matrices and determinants · Laplace transforms and Fourier series

An independent, free reviewer: not affiliated with the PRC or the Boards. Subject weights and passing rules are from the PRC examination programs and the laws (RA 9292, RA 7920); check the current PRC program before you file. Code questions follow the Philippine Electrical Code 2017 Part 1; check them against your own copy of the Code.