Exercise 13.1

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E|F) and P(F|E)

4, 7, 8, 9, 10, 12, 13, 17 2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 Find the mean deviation about the median for the data in Exercises 3 and 4.

A black and a red dice are rolled. (a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Height 95-105 105-115 115-125 125-135 135-145 145-155 in cms

30 12 10 boys

A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5} Find (i) P(E|F) and P(F|E) (ii) P(E|G) and P(G|E) (iii) P((E ∪ F)|G) and P((E ∩ F)|G)

Find the mean deviation about median for the following data : Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of 6 8 14 16 4 2 Girls

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

persons given below: Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 (in years)

[Hint Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval] 13.4.3 Limitations of mean deviation In a series, where the degree of variability is very high, the median is not a representative central tendency. Thus, the mean deviation about median calculated for such series can not be fully relied. The sum of the deviations from the mean (minus signs ignored) is more than the sum of the deviations from median. Therefore, the mean deviation about the mean is not very scientific.Thus, in many cases, mean deviation may give unsatisfactory results. Also mean deviation is calculated on the basis of absolute values of the deviations and therefore, cannot be subjected to further algebraic treatment. This implies that we must have some other measure of dispersion. Standard deviation is such a measure of dispersion.

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’. In each of the Exercises 16 and 17 choose the correct answer:

If P(A) = 2 , P(B) = 0, then P(A|B) is

(A) 0 (B) 1 (C) not defined (D) 1

If A and B are events such that P(A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B (B) A = B (C) A ∩ B = φ (D) P(A) = P(B)

Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49 Find the mean deviation about the mean for the data in Exercises 5 and 6.

If P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find (i) P(A ∩ B) (ii) P(A|B) (iii) P(A ∪ B)

Evaluate P(A ∪ B), if 2P(A) = P(B) = 5 13 and P(A|B) = 2

If P(A) = 6 11 , P(B) = 5 11 and P(A ∪ B) 7 11= , find (i) P(A∩ B) (ii) P(A|B) (iii) P(B|A) Determine P(E|F) in Exercises 6 to 9.

6 3 5

A coin is tossed three times, where (i) E : head on third toss , F : heads on first two tosses (ii) E : at least two heads , F : at most two heads (iii) E : at most two tails , F : at least one tail

Find the mean deviation about the median for the data in Exercises 7 and 8.

12 15

2 2 6

Two coins are tossed once, where (i) E : tail appears on one coin, F : one coin shows head (ii) E : no tail appears, F : no head appears

Find the mean deviation about the mean for the data in Exercises 9 and 10.

A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

Income per0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 day in `

of persons

Mother, father and son line up at random for a family picture E : son on one end, F : father in middle