Q.1.1.1 What is the probability of randomly selecting a male respondent from the sample? Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers Checkers? Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred supermarket is Pick n Pay? Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers Woolworths? Q.1.1.5 What is the probability of selecting a respondent who does not prefer Woolworths? Q.1.2 A recent survey found that the probability that a student at a particular educational institution is doing a BCom degree is 0.85. The same survey found that the probability that a student at the institution is male and is doing a BCom degree is 0.25. Given this information, what is the probability that a student at the institution is male, given that the student is doing a BCom degree? Q.1.3 Draw a Venn diagram to illustrate the union of two events, A and B, where A and B are mutually exclusive.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
| preferred supermarket | ||||
| pick n pay | checkers | woolworths | Total | |
| No. of females | 70 | 60 | 125 | 225 |
| no. of males | 70 | 50 | 25 | 145 |
| Total | 140 | 110 | 150 | 400 |
Q.1.1.1 What is the
Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers Checkers?
Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred supermarket is Pick n Pay?
Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers Woolworths?
Q.1.1.5 What is the probability of selecting a respondent who does not prefer Woolworths?
Q.1.2 A recent survey found that the probability that a student at a particular educational institution is doing a BCom degree is 0.85. The same survey found that the probability that a student at the institution is male and is doing a BCom degree is 0.25. Given this information, what is the probability that a student at the institution is male, given that the student is doing a BCom degree?
Q.1.3 Draw a Venn diagram to illustrate the union of two
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