class IX Probability

                                                            Probability

                                                      Class IX-Math

                                                   MISCELLANEOUS 

1.Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

    Outcome           3 heads      2 heads    1 head       No head

    Frequency           23               72           77              28

   If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

2. Two coins are tossed simultaneously 100 times and we get the following outcomes:

    (a) No head=30 (b) One head=20 (c) two heads=50

    Find the probability of each event.

3. Two coins tossed simultaneously, find the probability of getting one or more tail.

4.  A die is thrown. Find the probability of getting an odd number.

5. A coin is tossed 15 times and observed that 11 times head comes up. Find the probability that a tail

comes up.

6. The marks obtained by the students of two sections of a school in English are given in the following

table.  

               Marks                               Number of students

               0-20                                            8

             20-40                                           12

            40-60                                           30

           60-80                                            30

        80-100                                            10  

        Total                                                90

(a) Find the probability that a student obtained less than 40 in English test.

(b) Find the probability that a student obtained marks 80 or above.

7.A die is thrown 42 times and the outcomes listed in the form of a table as follows:

Number of times these           1       2         3            4         5            6

scores turn up

Number of times a die is       5       2         7          14       10            4

thrown

Find the probability that 5 turn up.

8. Without looking at the page the pencil is placed on one of these numbers i.e., the number is chosen at

random. What is the probability that digit in its unit place is 5?

Digit       01         2      3       4         5       6       7        8       9

f              24        17     29      45     60     70     78      83     85

9. Two coins are tossed simultaneously by 300 times and we get, Two heads: 135, One head: 63, No

head : 102. Find the probability of occurrence of each of these events.

10. A die is thrown 500 times with the frequencies for the outcomes, 1, 2, 3, 4, 5, 6 as given in the

following table.

Outcome                1        2        3       4        5         6

Frequency            80       75      90      75       85     95

Find the probability of getting an outcome less than 4.

11.Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome             3 heads     2 heads        1 heads         No head

Frequency                23           72                77                 28

If the three coins are simultaneously tossed again, compute the probability of coming up (a) 2 heads,

(b) no tail.

12. 1500 families with 2 children were selected randomly and the following data were recorded.

Number of girls in family                  2            1           0

Number of families                         475         814        211

Compute the probability of having

(a) Two girls (b) One girl (c) No girl (d) Also find the sum of these probabilities.

13.The king queen and jack of clubs are removed from a deck of 52 cards and then well shuffled. One

card is selected from the remaining card. Find the probability of getting.

(a) A heart (b) A king (c) The 10 of hearts.

14.A die is thrown 400 times, the frequency of outcomes 1, 2, 3, 4 5 and 6 are noted in frequency

distribution table given below:

Outcome            1        2         3         4         5        6  

Frequency         75      60       65       70       68      62

Find the probability of occurrence of (a) on odd number (b) a prime number.

15.A die is tossed 100 times and the data is recorded as below:

Outcome                  1       2          3        4        5         6

Frequency               20     15        20      15      20      10

(a) what is the probability that we get an even number in a trail?

(b) what is the probability of getting a number less than 3?