2 Marks Questions

Question 12 Marks

The percentages of marks obtained by a student in six unit tests are given below:

Unit test	$I$	$II$	$III$	$IV$	$V$	$VI$
Percentage of marks obtained	$53$	$72$	$28$	$46$	$67$	$59$

A unit test is selected at random. What is the probability that the student gets more than $60\%$ marks in the test?

Answer

Number of tests in which he gets more than $60\%$ marks $= 2$
Total numbers of tests $= 6$
$\therefore$ Required probability $=\frac{\text{Number of tests in which he gets more than 60% marks}}{\text{Total number of trials}}$
$=\frac{2}{6}=\frac{1}{3}$

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Question 22 Marks

The marks obtained by 90 students of a school in mathematics out of 100 are given as under:

Marks	0 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 and above
Number of students	7	8	12	25	19	10	9

From these students, a student is chosen at random.
What is the probability that the chosen student:

Gets 20% or less marks?
Gets 60% or more marks?

Answer

Total number of patients = 90

Probability that the chosen student gets 20% or less marks $=\frac{7}{90}$
Probability that the chosen student gets 60% or more marks $=\frac{10+9}{90}=\frac{19}{90}$

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Question 32 Marks

12 Packets of salt, each marked 2kg, actually contained the following weights (in kg) of salt:
1.950, 2.020, 2.060, 1.980, 2.030, 1.970, 2.040, 1.990, 1.985, 2.025, 2.000, 1.980.
Out of these packets, one packet is chosen at random.
What is the probability that the chosen packet contains more than 2kg of salt?

Answer

Total number of salt packets = 12
Number of packets containing more than 2kg of salt = 5
Therefore,
Probability that the chosen packet contains more than 2kg of salt $=\frac{\text{No. of packets containing more than 2kg of salt}}{\text{Total number of salt packets}}$
$=\frac{5}{12}$

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Question 42 Marks

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed, as under:

Types of vehicle	Two-wheelers	Three-wheelers	Four-wheelers
Frequency	84	68	88

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

Answer

Total number of vehicles going past the crossing = 240
Number of two-wheelers = 84
Let E be the event that the selected vehicle is a two-wheeler. Then,
required probability = P(E) $=\frac{84}{240}=0.35$

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