10th Probability Test sample paper

Probability

1.     A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail: 545 compute the probability for each event.

2.     Two coins are tossed simultaneously 500 times, and we get- Two heads: 105 times,
One head: 275 times, No head: 120 times, find the probability of occurrence of each of these events.

3.     A die is thrown 1000 times with the frequencies for the outcome 1, 2, 3, 4, 5 and 6 as given in the following table:

Outcome	1	2	3	4	5	6
Frequency	179	150	157	149	1175	190

Find the probability of getting each outcome.

4.     The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times.
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?

5.     The percentage (%) of the marks obtained by a student in the monthly unit test are given below:

Unit test	I	II	III	IV	V
Percentage (%) of the marks obtained	69	71	73	68	74

Based on this data, find the probability that the student gets more than 70% marks in a unit test.

6.     An insurance company selected 2000 drivers at random (i.e. without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:

Age of  drivers (in years	Accidents in one year
	0	1	2	3	Over 3
18-29	440	160	110	61	35
30-50	505	125	60	22	18
Above 50	360	45	35	15	9

Find the probabilities of the following events for a driver chosen at random from the city:
(i) Being 18-29 years of age and having exactly 3 accidents in one year.
(ii) Being 30-50 years of age and having one or more accidents in a year.
(iii) Having no accidents in one year.

7.     In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

8.     1500 families with 2 children were selected randomly, and the following data were recorded:

Numbers of girls in a family	2	1	0
Number of families	475	814	211

Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl.

9.     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.

10.   An organization selected 2400families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family, the information gathered is listed in the table below:

Monthly in come  (in Rs)	Vehicles per family
	0	1	2	Above 2
Less than 7000	10	160	25	0
7000-10000	0	305	27	2
10000-13000	1	535	29	1
13000-16000	2	469	59	25
16000 or more	1	579	82	88

Suppose a family is chosen. Find the probability that the family chosen is
(i) Earning Rs 10000-13000 per month and owing exactly 2 vehicles.
(ii) Earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) Earning less than Rs 7000 per month and does not own any vehicle.
(iv) Earning Rs 13000-16000 per month and owning more than 2 vehicles.
(v) Owning not more than 1 vehicle.
11.   Eleven bags of wheat flour, each marked 5 kg, actually contained following weights of flour (in kg): 4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00 find the probability that any of these Bags chosen at random contains more than 5 kg of flour.