Exercise 13.2

If P(A) 3 5= and P (B) 1 5= , find P (A ∩ B) if A and B are independent events.

6, 7, 10, 12, 13, 4, 8, 12 2. First n natural numbers

Events A and B are such that P (A) = 1 2 , P(B) = 7 12 and P(not A or not B) = 1 4 . State whether A and B are independent ?

The diameters of circles (in mm) drawn in a design are given below: Diameters 33-36 37-40 41-44 45-48 49-52

Calculate the standard deviation and mean diameter of the circles. [ Hint First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)

A die is tossed thrice. Find the probability of getting an odd number at least once.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red. 14. Probability of solving specific problem independently by A and B are 1 2 and 1 respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ? (i) E : ‘the card drawn is a spade ’ F : ‘ the card drawn is an ace ’ (ii) E : ‘the card drawn is black’ F : ‘the card drawn is a king’ (iii) E : ‘the card drawn is a king or queen’ F : ‘the card drawn is a queen or jack ’ .

In a hostel, 60% of the students read Hindi newspaper , 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English newspapers. (b) If she reads Hindi newspaper , find the probability that she reads English newspaper. (c) If she reads English newspaper , find the probability that she reads Hindi newspaper. Choose the correct answer in Exercises 17 and 18.

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is (A) 0 (B) 1 / 3 (C) 1 / 12 (D) 1

Two events A and B will be independent, if (A) A and B are mutually exclusive (B) P(A′B′) = [1 - P(A)] [1 - P(B)] (C) P(A) = P(B) (D) P(A) + P(B) = 1

playing cards. Find the probability that both the cards are black.

First 10 multiples of 3

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved

oranges out of which 12 are good and 3 are bad ones will be approved for sale.

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin ’ and B be the event ‘3 on the die ’. Check whether A and B are independent events or not.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even, ’ and B be the event, ‘the number is red ’. Are A and B independent?

98 102 104 109

2 6 3 3

Let E and F be events with P(E) 5= , P(F) 3 10= and P (E ∩ F) = 1 5 . Are E and F independent?

Find the mean and standard deviation using short-cut method.

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.

Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210

5 10 3 5 2

Given that the events A and B are such that P(A) = 1 2 , P(A ∪ B) = 3 5 and P(B) = p. Find p if they are (i) mutually exclusive (ii) independent.

Classes 0-10 10-20 20-30 30-40 40-50

16 6

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find (i) P(A ∩ B) (ii) P(A ∪ B) (iii) P (A|B) (iv) P (B|A)

If A and B are two events such that P(A) = 1 4 , P (B) = 1 2 and P(A ∩ B) = 1 8 , find P (not A and not B).

Find the mean, variance and standard deviation using short-cut method Height 70-75 75-80 80-85 85-90 90-95 95-100 100-105105-110 110-115 in cms No. of 3 4 7 7 15 9 6 6 3 children