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Higher Engineering Mathematics

John Bird

Chapter 59

Probability - all with Video Answers

Educators

Chapter Questions

02:09

Problem 1

Determine the probabilities of selecting at random (a) a man, and (b) a woman from a crowd containing 20 men and 33 women.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:03

Problem 2

Find the expectation of obtaining a 4 upwards with three throws of a fair dice.

Willis James
Willis James
Numerade Educator
01:41

Problem 3

Calculate the probabilities of selecting at random:
(a) the winning horse in a race in which ten horses are running,
(b) the winning horses in both the first and second races if there are ten horses in each race.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:30

Problem 4

. The probability of a component failing in one year due to excessive temperature is $\frac{1}{20}$, due to excessive vibration is $\frac{1}{25}$ and due to excessive humidity is $\frac{1}{50}$. Determine the probabilities that during a one-year period a component: (a) fails due to excessive temperature and excessive vibration, (b) fails due to excessive vibration or excessive humidity, and (c) will not fail because of both excessive temperature and excessive humidity.

Jonathon Brumley
Jonathon Brumley
Numerade Educator
03:56

Problem 5

A batch of 100 capacitors contains 73 which are within the required tolerance values, 17 which are below the required tolerance values, and the remainder are above the required tolerance values. Determine the probabilities that when randomly selecting a capacitor and then a second capacitor: (a) both are within the required tolerance values when selecting with replacement, and (b) the first one drawn is below and the second one drawn is above the required tolerance value, when selection is without replacement.

Sikandar Baig
Sikandar Baig
Numerade Educator
02:10

Problem 6

A batch of 40 components contains five which are defective. A component is drawn at random from the batch and tested and then a second component is drawn. Determine the probability that neither of the components is defective when drawn (a) with replacement, and (b) without replacement.

Sikandar Baig
Sikandar Baig
Numerade Educator
02:10

Problem 7

A batch of 40 components contains five which are defective. If a component is drawn at random from the batch and tested and then a second component is drawn at random, calculate the probability of having one defective component, both with and without replacement.

Sikandar Baig
Sikandar Baig
Numerade Educator
02:20

Problem 8

A box contains 74 brass washers, 86 steel washers and 40 aluminium washers. Three washers are drawn at random from the box without replacement. Determine the probability that all three are steel washers.

Sikandar Baig
Sikandar Baig
Numerade Educator
02:52

Problem 9

. For the box of washers given in Problem 8 above, determine the probability that there are no aluminium washers drawn, when three washers are drawn at random from the box without replacement.

Sikandar Baig
Sikandar Baig
Numerade Educator
03:00

Problem 10

For the box of washers in Problem 8 above, find the probability that there are two brass washers and either a steel or an aluminium washer when three are drawn at random, without replacement.

Sikandar Baig
Sikandar Baig
Numerade Educator
01:20

Problem 11

Calculate the number of permutations there are of: (a) five distinct objects taken two at a time, (b) four distinct objects taken two at a time.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:22

Problem 12

Calculate the number of combinations there are of (a) five distinct objects taken two at a time, (b) four distinct objects taken two at a time.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:15

Problem 13

A class has 24 students. Four can represent the class at an exam board. How many combinations are possible when choosing this group?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
00:58

Problem 14

In how many ways can a team of 11 be picked from 16 possible players?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
00:20

Problem 15

An outdoor degree ceremony is taking place tomorrow, 5 July, in the hot climate of Dubai. In recent years it has rained only 2 days in the four-month period June to September. However, the weather forecaster has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain $85 \%$ of the time. When it doesn't rain, he incorrectly forecasts rain $15 \%$ of the time. Determine the probability that it will rain tomorrow.

Nick Johnson
Nick Johnson
Numerade Educator