August
1997 QUESTION 2 Total Marks: 20 Marks |
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| 2. | (a) A string of three bits is obtained randomly. | ||
| (i) List all the elements of the sample space. | [1] | ||
| (ii) Let A be the event
that the string contains an odd number of 1s, and let B be the event that the
string starts with a 1. Are a and B independent? Explain your answer using probability calculations. |
[4] | ||
| (b) Suppose that three computer boards in a production run of 40 are defective. A sample of four is to be selected to be checked for defects. | |||
| (i) How many different samples can be chosen? | [2] | ||
| (ii) How many samples will contain at least one defective board? | [2] | ||
| (iii) What is the probability that a randomly chosen sample of four contains at least one defective board? | [1] | ||
| (c) A coin is tossed 10 times. In each case, the outcome H (for hear), or T (for tail) is recorded. | |||
| (i) What is the total number of possible outcomes of the coin-tossing experiment? | [2] | ||
| (ii) In how many of the possible outcomes are exactly five heads obtained? | [2] | ||
| (iii) In how many of the possible outcomes are at least nine heads obtained? | [2] | ||
| (iv) In how many of the possible outcomes are at most one head obtained? | [2] | ||
| (v) In how many of the possible outcomes are at least one tail obtained? | [2] | ||