A die is thrown once. Find the probability of getting "at most 2."

1

(a)

S = {1, 2, 3, 4, 5, 6}
n(S) = 6
A = {1, 2}
n(A) = 2
\(P\left( A \right) =\frac { n\left( A \right) }{ n\left( S \right) } =\frac { 2 }{ 6 } =\frac { 1 }{ 3 } \)

Cards marked with number 3, 4, 5,.........., 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.

1

(a)

Possible outcomes are 4, 9, 16, 25, 36, 49, i.e. 6.
\(\Rightarrow\) P(perfect square number) =  \(\frac{6}{48}​​\)or \(\frac{1}{8}​​\)

What is the probability that a non-leap year has 53 Mondays?

1

(a)

There are 365 days in a non-leap year.
\(\because\) 365 days = 52 weeks + 1 day
\(\therefore\) One day can be M, T, W, Th, F, S, S = 7
\(\therefore\) P(53 Mondays in non-leap year) = \(\frac{1}{7}\).

Two different dice are tossed together. Find the probability that the product of the number on the top of the dice is 6.

1

(a)

Product of 6 are (1, 6); (2,3); (6, 1); (3,2)
No. of possible out comes = 4
Total number of chances = 6\(\times\)6 = 36
P (Product of 6) = \(\frac{4}{36} \) = \(\frac{1}{9}\).

A girl calculates the probability of her winning the game in a match and find it 0.08.What is the probability of her losing the game?

1

(a)

P(winning the game) = 0.08
P(losing the game) = 1- 0.08 = 0.92

For any event E, P(E)+P(\(\overset { - }{ E } \))

1

(a) True

(b) False

Ace, King,Queen and Jack are called face cards.

1

(a) True

(b) False

Set of all possible outcomes of the experiment is called the sample space.

1

(a) False

(b) True

In a lottery, there are 10 prizes and 45 blanks, then probability of getting a prize is \(2\over11\).

1

(a) False

(b) True

Probability of an event cannot be negative.

1

(a) False

(b) True

The probability of an event that is certain to happen is ___________Such an event is called_____________

2

(a)

1, sure event. (e.g. The event of getting a number less than 7 in a single throw of a die is a sure event and its probability is 1.)

Two coins are tossed simultaneously. Find the probability of getting exactly one head.

2

(a)

When two coins are tossed simultaneously
Total number of number of outcomes = {HH, HT, TH, TT}
Total number of outcomes = 4
Favourable outcomes = {HT, TH} = 2
Probability of getting exactly one head = \(\frac{2}{4}=\frac{1}{2}\)

The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?

2

(a)

probability that it will not rain tomorrow
 = 1 - Probability that it will rain tomorrow = 1 - 0.85 = 0.15

If an event occurs surely, then find its probability.

2

(a)

Probability of sure event = 1

If from the face cards of a playing cards, one card is picked up at random, then find the probability that the drawn card is a queen.

2

(a)

Here, total number of face cards are 12
Number of queens are 4
Therefore Required probability = \(\frac { 4 }{ 12 } =\frac { 1 }{ 3 } \)

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

3

(a)

Five cards - the ten, jack, queen, king and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put a side, what is the probability that the second card picked up is
(a) an ace?
(b) a queen?

3

(a)

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the jack of hearts.

3

(a)

A coin is tossed two times. Find the probability of getting at least one head.

3

(a)

An unbiased die is thrown, what is the probability of getting a multiple of 3.

3

(a)

1. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is

   (i) a king or a jack   (ii) a non-ace

   (iii) a red card   (iv) neither a king nor a queen

   5

   (a)

2. Two different dice are thrown together. Find the probability of:

   (i) getting a number greater than 3 on each die

   (ii) getting a total of 6 or 7 of the numbers on two dice

   5

   (a)

1. A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a
   (i) triangle  (ii) square
   (iii) square of blue colour  (iv) triangle of red colour

   5

   (a)

2. Two unbiased coins are tossed simultaneously. find the probability of getting
   (i) no heads
   (ii) atmost one tail
   (iii) one tail
   (iv) one head and one tail

   5

   (a)