5 Marks Questions

Question 15 Marks

The table given below shows the ages of 75 teachers in a school.

Age (in years)	18 - 29	30 - 39	40 - 49	50 - 59
Number of teachers	3	27	37	8

A teacher from this school is chosen at random. What is the probability that the selected teacher is:

40 or more than 40 years old?
Of an age lying between 30 - 39 years (including both)?
18 years or more and 49 years or less?
18 years or more old?
Above 60 years of age?

Note: Here 18 - 29 means 18 or more but less than or equal to 29.

Answer

Total number of teachers = 75

Probability that the selected teachers is 40 or more than 40 years old $=\frac{37+8}{75}=\frac{45}{75}=\frac{3}{5}$
Probability that the selected teachers is of an age lying between 30 - 39 years (including both) $=\frac{27}{75}=\frac{9}{25}$
Probability that the selected teachers is 18 years or more and 49 years or less $=\frac{3+27+37}{75}=\frac{67}{75}$
Probability that the selected teachers is 18 years or more old $=\frac{3+27+37+8}{75}=\frac{75}{75}=1$
Probability that the selected teachers is above 60 years of age $=\frac{0}{75}=0$

View full question & answer→

Question 25 Marks

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Age (in years)	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
Number of patients	90	50	60	80	50	30

One of the patients is selected at random.
What is the probability that his age is:

30 years or more but less than 40 years?
50 years or more but less than 70 years?
10 years or more but less than 40 years?
10 years or more?
Less than 10 years?

Answer

Total number of patients = 360

Probability that the age selected patients is 30 years or more but less than 40 years $=\frac{60}{360}=\frac{1}{6}$
Probability that the age selected patients is 50 years or more but less than 70 years $=\frac{50+30}{360}=\frac{80}{360}=\frac{2}{9}$
Probability that the age selected patients is 10 years or more but less than 40 years $=\frac{90+50+60}{360}=\frac{200}{360}=\frac{5}{9}$
Probability that the age selected patients is 10 years or more$=1$
Probability that the age selected patients is less than 10 years $=0$

View full question & answer→

Question 35 Marks

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

Monthly income(in ₹)	Number of vehicles per family
Monthly income(in ₹)	0	1	2	3 or more
Less than ₹ 25000	10	160	25	0
₹ 25000 - ₹ 30000	0	305	27	2
₹ 30000 - ₹ 35000	1	535	29	1
₹ 35000 - ₹ 40000	2	469	59	25
₹ 40000 or more	1	579	82	88

Suppose a family is chosen at random. Find the probability that the family chosen is:

Earning ₹ 25000 - ₹ 30000 per month and owning exactly 2 vehicles.
Earning ₹ 40000 or more per month and owning exactly 1 vehicle.
Earning less than ₹ 25000 per month and not owning any vehicle.
Earning ₹ 35000 - ₹ 40000 per month and owning 2 or more vehicles.
Owning not more than 1 vehicle.

Answer

Probability that a family chosen is earning ₹ 25000 - ₹ 30000 per month and owning exactly 2 vehicles $=\frac{27}{2400}=\frac{9}{800}$
Probability that a family chosen is Earning ₹ 40000 or more per month and owning exactly 1 vehicle $=\frac{579}{2400}=\frac{193}{800}$
Probability that a family chosen is earning less than ₹ 25000 per month and not owning any vehicle $=\frac{10}{2400}=\frac{1}{240}$
Probability that a family chosen is earning ₹ 35000 - ₹ 40000 per month and owning 2 or more vehicles = Probability(Families owning 2 vehicles + Families owning 3 or more vehicles)

$=\frac{59+25}{2400}$

$=\frac{84}{2400}$

$=\frac{7}{200}$

Probability that a family chosen is owning not more than 1 vehicle = Probability(Families owning 0 vehicle + Families owning 1 vehicle)

$=\frac{(10+0+1+2+1)+(160+305+535+469+579)}{2400}$

$=\frac{14+2048}{2400}$

$=\frac{2062}{2400}$

$=\frac{1031}{1200}$

View full question & answer→

Maths 5 Marks Questions

Test yourself on this topic