Probability 311
Now try the following Practice Exercise
Practice Exercise 130 Laws of probability
(answers on page 354)
1. The probability that component A will operate
satisfactorily for 5 years is 0.8 and that B will
operate satisfactorily over that same period of
time is 0.75. Find the probabilities that in a 5
year period
(a) both components will operate
satisfactorily.
(b) only component A will operate
satisfactorily.
(c) only component B will operate
satisfactorily.
2. In a particular street, 80% of the houses have
landline telephones. If two houses selected at
random are visited, calculate the probabilities
that
(a) they both have a telephone.
(b) one has a telephone but the other does
not.
3. Veroboard pins are packed in packets of 20
by a machine. In a thousand packets, 40 have
less than 20 pins. Find the probability that if 2
packets are chosen at random, one will contain
less than 20 pins and the other will contain 20
pins or more.
4. A batch of 1 kW fire elements contains 16
which are within a power tolerance and 4
which are not. If 3 elements are selected at random from the batch, calculate the probabilities
that
(a) all three are within the power tolerance.
(b) two are within but one is not within the
power tolerance.
5. An amplifier is made up of three transistors, A, B and C. The probabilities of A, B
or C being defective are 1/20, 1/25 and
1/50, respectively. Calculate the percentage of
amplifiers produced
(a) which work satisfactorily.
(b) which have just one defective transistor.
6. A box contains 14 40 W lamps, 28 60 W lamps
and 58 25 W lamps, all the lamps being of the
same shape and size. Three lamps are drawn at
random from the box, first one, then a second,
then a third. Determine the probabilities of
(a) getting one 25 W, one 40 W and one 60 W
lamp with replacement.
(b) getting one 25 W, one 40 W and one 60 W
lamp without replacement.
(c) getting either one 25 W and two 40 W
or one 60 W and two 40 W lamps with
replacement.
Now try the following Practice Exercise
Practice Exercise 130 Laws of probability
(answers on page 354)
1. The probability that component A will operate
satisfactorily for 5 years is 0.8 and that B will
operate satisfactorily over that same period of
time is 0.75. Find the probabilities that in a 5
year period
(a) both components will operate
satisfactorily.
(b) only component A will operate
satisfactorily.
(c) only component B will operate
satisfactorily.
2. In a particular street, 80% of the houses have
landline telephones. If two houses selected at
random are visited, calculate the probabilities
that
(a) they both have a telephone.
(b) one has a telephone but the other does
not.
3. Veroboard pins are packed in packets of 20
by a machine. In a thousand packets, 40 have
less than 20 pins. Find the probability that if 2
packets are chosen at random, one will contain
less than 20 pins and the other will contain 20
pins or more.
4. A batch of 1 kW fire elements contains 16
which are within a power tolerance and 4
which are not. If 3 elements are selected at random from the batch, calculate the probabilities
that
(a) all three are within the power tolerance.
(b) two are within but one is not within the
power tolerance.
5. An amplifier is made up of three transistors, A, B and C. The probabilities of A, B
or C being defective are 1/20, 1/25 and
1/50, respectively. Calculate the percentage of
amplifiers produced
(a) which work satisfactorily.
(b) which have just one defective transistor.
6. A box contains 14 40 W lamps, 28 60 W lamps
and 58 25 W lamps, all the lamps being of the
same shape and size. Three lamps are drawn at
random from the box, first one, then a second,
then a third. Determine the probabilities of
(a) getting one 25 W, one 40 W and one 60 W
lamp with replacement.
(b) getting one 25 W, one 40 W and one 60 W
lamp without replacement.
(c) getting either one 25 W and two 40 W
or one 60 W and two 40 W lamps with
replacement.