3 Mark Question

Question 13 Marks

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One heads: 290 times
No heads: 115 times
Find the probability of occurrence of each of these events.

Answer

Probability (E) $=\frac{\text{Number of trialsin which events happen}}{\text{Total no. of trials}}$
P(getting two heads) $=\frac{95}{500}=0.19$
P(getting one tail) $=\frac{290}{500}=0.58$
P(getting no head) $=\frac{115}{500}=0.23$

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Question 23 Marks

To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:

Opinion	Like	Dislike
Number of students	135	65

Find the probability that a student chosen at random:

Likes Mathematics
Does not like it.

Answer

Probability that a student likes mathematics

$=\frac{\text{Favorable out come}}{\text{Total out come}}$

$=\frac{135}{200}$

$=0.675$

Probability that a student does not like mathematics

$=\frac{\text{Favorable out come}}{\text{Total out come}}$

$=\frac{65}{200}$

$=0.325$

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Question 33 Marks

The percentage of marks obtained by a student in the monthly unit tests are given below:

Unit Test	I	II	III	IV	V
Percentage of Mark Obtained	69	71	73	68	76

Find the probability that the student gets:

More than 70% marks.
Less than 70% marks.
A distinction

Answer

Let E be the event of getting more than 70% marks.

No of times E happens = 3

Probability(getting more than 70%)

$=\frac{\text{Number of times student got more than 70}}{\text{Total no. of exams taken}}$

$=\frac{3}{5}=0.6$

Let F be the event of getting less than 70% marks

No of times F happen = 2

Probability(getting more than 70%)

$=\frac{\text{Number of times student got more than 70}}{\text{Total no. of exams taken}}$

$=\frac{2}{5}=0.4$

Let G be the event of getting distinction

No of times G happen = 1

Probability(getting distinction)

$=\frac{\text{Number of times student got distinction}}{\text{Total no. of exams taken}}$

$=\frac{1}{5}=0.2$

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Question 43 Marks

Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in Kg).

4.97

5.05

5.08

5.03

5

5.06

5.08

4.98

5.04

5.07

5

Find the probability that any of these bags chosen at random contains more than 5kg of flour.

Answer

Number of bags weighting more than 5kg = 7 Total no of bags = 11 Probability of having more than 10kg of rice $=\frac{\text{No. of bages weighting more than 5kg}}{\text{Total no. of bages}}$
$=\frac{7}{11}=0.63$

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Question 53 Marks

A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail = 545.
Compute the probability of each event.

Answer

It is given that the coin is tossed 1000 times. The number of trials is 1000. Let us denote the event of getting head and of getting tails be E and F respectively. Then, Number of trials in which the E happens = 455 So, Probability of E $=\frac{\text{Number of even theads}}{\text{Total no. of trials}}$$\text{i.e}.\text{P(E)}=\frac{455}{1000}=0.455$
Similarity, the probability of the event getting a tail $=\frac{\text{Number of tails}}{\text{Total no. of trials}}$$\text{i.e.}\text{P(F)}=\frac{545}{1000}=0.545$

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