Impossible Events

Q. If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.

Q.

If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his

chance of winning prize are

1. 

2. 

3. 

4. None of these

Q. An experiment consists of recording boy–girl composition of families with $2$ children.
$\left(i\right)$ What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ?
$\left(ii\right)$ What is the sample space if we are interested in the number of girls in the family ?

Q.

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

Q. Mark the correct alternative in the following question:

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is

$\left(\mathrm{a}\right)\frac{15}{29}\left(\mathrm{b}\right)\frac{15}{56}\left(\mathrm{c}\right)\frac{45}{196}\left(\mathrm{d}\right)\frac{135}{392}$

Q. Describe the sample space for the indicated experiment :
$2$ boys and $2$ girls are in Room $X$, and $1$ boy and $3$ girls in Room $Y$.
Specify the sample space for the experiment in which a room is selected and then a person.

Q. A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
(a) 1/2
(b) 1/8
(c) 3/8
(d) None of these

Q. From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is
(a) 6/25
(b) 1/4
(c) 1/6
(d) 2/5

Q. A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.

Q.

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Q.

India need to score 100 runs in 8 balls to win Harsha Bhogle's comments, "It s an impossible event that India wins”. Comment on the validity of his statement.

1. True

2. False

Q. A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
(a)

(b)

(c)

(d)

Q. The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.

Q. The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.

Q.

India need to score 100 runs in 8 balls to win Harsha Bhogle's comments, "It s an impossible event that India wins”. Comment on the validity of his statement.

1. True

2. False

Q.

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

Q. A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
(a) $\frac{64}{64}$

(b) $\frac{49}{64}$

(c) $\frac{40}{64}$

(d) $\frac{24}{64}$