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#### Question 1:

A coin is tossed 1000 times with the following frequencies:

When a coin is tossed at random, what is the probability of getting (i) a head? (ii) a tail?

Total number of times a coin is tossed = 1000
Number of times a head comes up = 445
Number of times a tail comes up = 555

(i) Probability of getting a head =

(ii) Probability of getting a tail =

#### Question 2:

A die is thrown 100 times and outcomes are noted as given below:

 Outcome: 1 2 3 4 5 6 Frequency: 21 9 14 23 18 15
If a die is thrown at random, find the probability of getting a/an.
(i) 3
(ii) 5
(iii) 4
(iv) Even number
(v) Odd number
(vi) Number less than 3.

Total number of trials = 100

Number of times "1" comes up = 21
Number of times "2" comes up = 9
Number of times "3" comes up = 14
Number of times "4" comes up = 23
Number of times "5" comes up = 18
Number of times "6" comes up = 15

(i) Probability of getting 3

=

(ii) Probability of getting 5

=

(iii) Probability of getting 4

=

(iv) Frequency of getting an even no. = Frequency of 2 + Frequency of 4 + Frequency of 6 = 9+ 23 + 15 = 47

Probability of getting an even no. =

(v) Frequency of getting an  odd no. = Frequency of 1 + Frequency of 3 + Frequency of 5 = 21+ 14 + 18 = 53

Probability of getting an odd no. =

(vi) Frequency of getting a no. less than 3 = Frequency of 1 + Frequency of 2= 21 + 9 = 30

Probability of getting a no. less than 3

=

#### Question 3:

A box contains two pair of socks of two colours (black and white). I have picked out a white sock. I pick out one more with my eyes closed. What is the probability that I will make a pair?

No. of socks in the box = 4
Let B and W denote black and white socks respectively.
Then we have:
S = {B,B,W,W}

If a white sock is picked out, then the total no. of socks left in the box = 3
No. of white socks left = 2-1 =1

Probability of getting a white sock

=

#### Question 4:

Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:

If same pair of coins is tossed at random, find the probability of getting (i) Two heads (ii) One head (iii) No head.

Number of trials = 500
Number of outcomes of two heads (HH) =  105
Number of outcomes of one head (HT or TH) =  275
Number of outcomes of no head (TT) =  120

(i) Probability of getting two heads =

(ii) Probability of getting one head =

(iii) Probability of getting no head =

#### Question 1:

An unbiased coin is tossed once, the probability of getting head is

(a) $\frac{1}{2}$                                  (b) 1                                         (c) $\frac{1}{3}$                                  (d) $\frac{1}{4}$

Tossing a coin, either we get a head (H) or a tail (T). So, the probability of getting a head is $\frac{1}{2}$.
Hence, the correct option is (a).

#### Question 2:

There are 10 cards numbered from 1 to 10. A card is drawn randomly. The probability of getting
an even numbered card is

(a) $\frac{1}{10}$                                  (b) $\frac{1}{5}$                                         (c) $\frac{1}{2}$                                  (d) $\frac{2}{5}$

The number on the cards are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
The even numbers on the cards are 2, 4, 6, 8, 10.
∴ Probability of getting an even numbered card =

$=\frac{5}{10}=\frac{1}{2}$
Hence, the correct option is (c).

#### Question 3:

A dice is rolled. The probability of getting an even prime is

(a) $\frac{1}{6}$                                  (b) $\frac{1}{3}$                                         (c) $\frac{1}{2}$                                  (d) $\frac{5}{6}$

The possible numbers on a dice are 1, 2, 3, 4, 5, 6.
There is only one even prime number which is 2.
∴ Probability of getting an even prime = $=\frac{1}{6}$

Hence, the correct option is (a).

#### Question 4:

There are 100 cards numbered from 1 to 100 in a box. If a card is drawn from the box and
the probability of an event is $\frac{1}{2}$, then the number of favourable cases to the event is

(a) 20                                         (b) 25                                          (c) 40                                             (d) 50

Here, $\frac{50}{100}=\frac{1}{2}$.
So, if the the probability of an event is $\frac{1}{2}$, then the number of favourable cases has to be 50.
Hence, the correct option is (d).

#### Question 5:

When a dice is thrown, the total number of possible outcomes is

(a) 6                                         (b) 1                                          (c) 3                                             (d) 4

The number on the faces of a dice are 1, 2, 3, 4, 5, and 6.
∴ Number of possible outcomes = 6
Hence, the correct option is (a).

#### Question 6:

There are 10 marbles in a box which are marked with the distinct numbers from 1 to 10.
A marble is drawn randomly. The probability of getting prime numbered marble is

(a) $\frac{1}{2}$                                         (b) $\frac{2}{5}$                                          (c) $\frac{9}{3}$                                             (d) $\frac{3}{10}$

The numbers marked on the marbles are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
Here, the prime numbers (favourable outcomes) are 2, 3, 5, and 7.
∴ Number of favourable outcomes = 4
Therefore
Probability of getting prime numbered marble = $\frac{4}{10}=\frac{2}{5}$
Hence, the correct option is (b).

#### Question 7:

The probability of getting a red card from a well shuffled pack of cards is

(a) $\frac{1}{4}$                                         (b) $\frac{1}{2}$                                      (c) $\frac{3}{4}$                                             (d) $\frac{1}{3}$

There are 52 cards in a standard deck. There are four different suits Diamonds (red), Clubs (black)
, Hearts (red), and Spades (black) each containing 13 cards.

∴ Number of red cards (favourable outcomes) = 13 + 13 = 26
Therefore
Probability of getting a red card = $\frac{26}{52}=\frac{1}{2}$
Hence, the correct option is (b).

#### Question 8:

A coin is tossed 100 times and head is obtained 59 times. The probability of getting a tail is

(a) $\frac{59}{100}$                                         (b) $\frac{41}{100}$                                      (c) $\frac{29}{100}$                                             (d) $\frac{43}{100}$

Number of all possible outcomes = 100
Number of head obtained = 59
Number of tail obtained (favourable outcomes) = 100 − 59 = 41

Therefore
Probability of getting a tail = $\frac{41}{100}$
Hence, the correct option is (b).

#### Question 9:

A dice is tossed 80 times and number 5 is obtained 14 times. The probability of not getting the number 5 is

(a) $\frac{7}{40}$                                         (b) $\frac{7}{80}$                                      (c) $\frac{33}{40}$                                             (d) None of these

Probability of getting 5 = $\frac{14}{80}=\frac{7}{40}$
Therefore
Probability of not getting 5 = $1-\frac{7}{40}=\frac{33}{40}$
Hence, the correct option is (c).

#### Question 10:

A bag contains 4 green balls, 4 red balls and 2 blue balls. If a ball is drawn from the bag, the
probability of getting neither green nor red ball is

(a) $\frac{2}{5}$                                         (b) $\frac{1}{2}$                                      (c) $\frac{4}{5}$                                             (d) $\frac{1}{5}$

Probability of getting neither green nor red ball = $\frac{2}{10}=\frac{1}{5}$