In each of the multiple choice questions ONE of the answers is CORRECT, except where stated otherwise (and then ONE is WRONG).

Q1. A travel agent has a list of 400 regular customers. Of these, 80 have been to France and 100 to Italy. There are 20 who have been to both France and Italy. The probability that one person selected at random from the list has not been either to France or to Italy is:

0.45
0.50
0.60
0.55
0.40

Q2. Twenty candidates apply for a job; 12 of these have degrees and 10 have some other qualification. There are 2 who have neither a degree nor another qualification. The probability that one selected at random from these 20 has both a degree and another qualification is:

0.30
0.10
0.17
0
0.20

Q3. A garage has 40 sports cars for sale, 16 of which have fog lights, 20 have reversing lights, 12 have spot lights, 4 have all three types of light, 8 have both reversing and spot lights, 6 have both fog and spot lights, and 8 have both fog and reversing lights. If a customer chooses one of these cars at random, the probability that it will have none of these three types of light is:

0.30
0.33
0.21
0.25
0.35

Q4. A squad of 20 players for a regional team is made up of 8 from club C, 7 from club M and 5 from club L. Seven players are selected at random from these 20. The probability that 3 are from C, 2 from M and 2 from L is:

0.152
0.015
0.303
0.076
0.001

Q5. A garage servicing motor vehicles has equipment which can detect the source of electrical faults. The mechanic using it detects fault F, but the supervisor knows that the test is not always reliable. He says that it is only 80% likely to detect correctly if the fault really is F, and it will “detect” fault F 10% of the time when the problem is in fact somewhere else. He also says that the fault really is F on 60% of occasions. The probability that the fault really is F when the mechanic has detected F is:

0.960
0.727
0.857
0.864
0.923

 

Q6. A sample survey of 120 households in a large town showed 8 households without a refrigerator, 12 who had two refrigerators in the household, and 100 who had one. The estimated mean and variance of the number of refrigerators per household are:

1.107, 0.1669
1.033, 0.1655
1.033, 0.409
1.033, 0.1669
1, 0.1655

Q7.The numbers of females r in litters of 4 offspring of a particular animal are summarised as follows: r = 0 1 2 3 4 f = 11 27 26 25 11.

The binomial distribution may not be a suitable model for these data because:

the probabilities of male and female births are not equal
the probability of a male birth is not constant
the data are over-dispersed
individual births within the same litter are not independent
the data were not all collected at the same time

Q8. The sum of independent geometric variables follows

a negative binomial
a binomial
a geometric
a Poisson
no simple distribution

Q9. In a single sampling scheme, the decision rule is to accept a sample of 7 items if 0 or 1 of these are faulty. The probability of accepting a batch of 7 when the population proportion faulty is ∏ is

(1 - ∏)⁷
∏(1 -∏)⁶
(1 - ∏)⁶(1 - 6∏)
(1 - ∏)⁶(1 + 6∏)
6∏(1 - ∏)⁶

Q10.The probability that it will take ten throws of a fair six-sided die before the face 6 first appears is:

0.032
0.194
0.323
0.162
0.135

Q11.Three fair dice are thrown. The probability of a total score of 6 is:

0.032
0.014
0.046
0.005
0.333

Q12.The probability that it will take ten throws of a fair six-sided die before the face 6 first appears is:

0.2256
0.0002
0.5000
0.0752
0.2500

Q13. Four friends meet by chance and dine together. Assuming that there is an equal probability of being born in any of the twelve months of the year, the probability that at least two of them have a birthday in the same month is

0.083
0.372
0.230
0.427
0.250

Q14. A batch of 30 items taken from an industrial production line contains 3 which are faulty. An inspector, not knowing this, selects 3 at random from the 30. The probability that at least two selected items are faulty is:

0.97200
0.02800
0.97980
0.02020
0.01995

Q15.Another name for the expected value of a random variable is:

mode
mean
median
mid-spread
average

Q16.The probability mass function of R is R = -1 0 1 2 P(R) = 0.3 0.2 0.2 0.3.
The expected value of R² is:

0.8
1.7
1.4
1.1
0.25

Q17.The variance of the above function R2 is:

2.41
5.00
1.15
2.20
2.50

Q18.Two random variables X,Y are jointly distributed. X may take the values 0, 1, 2 with probabilities 0.1, 0.5, 0.4 respectively. If X = 0, the conditional probabilities of Y taking the values 1, 3 are 0.6, 0.4 respectively. If X = 1, conditional probabilities for Y = 0, 2 are 0.3, 0.7 respectively. If X = 2, conditional probabilities for Y = 1, 2 are 0.8, 0.2 respectively.

0.90
0.35
0.35
0.45
0.43

Q19. In a random sample of n items from a population, r of them showed a particular characteristic. The estimate of the variance of p, the population proportion having this characteristic, is

[(r - 1)(n - r)]/[n(n - 1)]
r(n - r)/n²
r(n - r)/n³
(r - 1)(n - r)/(n - 1)
r(n - r)/n

Q20.A binomial random variable R has n = 16 and p = 0.75. The standardised value corresponding to R = 8 is:

1.33
-2.31
-1.33
-0.33
2.31

Q21.A survey is to be carried out in the central area of a town and the residential outskirts of it. The shopping habits and expenditure of people living there are to be studied. The best sampling method would be:

a stratified random sample of individuals
a stratified random sample of households
a simple random sample of individuals
a simple random sample of households
a systematic sample of individuals using a list of registered electors

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