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Maths 5 Marks Questions

Probability · Jharkhand Board (JAC) STD 9 (Jharkhand - English Medium). 3 questions.

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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:
$i. 40$ or more than $40$ years old$?$
$ii.$ Of an age lying between $30 - 39$ years $($including both$)?$
$iii. 18$ years or more and $49$ years or less$?$
$iv. 18$ years or more old$?$
$v.$  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 $= 75$
$i.$ Probability that the selected teachers is $40$ or more than $40$ years old $=\frac{37+8}{75}=\frac{45}{75}=\frac{3}{5}$
$ii.$ Probability that the selected teachers is of an age lying between $30 - 39$ years $($including both$)$ $=\frac{27}{75}=\frac{9}{25}$
$iii.$ Probability that the selected teachers is $18$ years or more and $49$ years or less $=\frac{3+27+37}{75}=\frac{67}{75}$
$iv.$ Probability that the selected teachers is $18$ years or more old $=\frac{3+27+37+8}{75}=\frac{75}{75}=1$
$v.$ Probability that the selected teachers is above $60$ years of age $=\frac{0}{75}=0$
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Question 25 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
$0$
$1$
$2$
$3$ 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:
$i.$ Earning $₹ 25000 - ₹ 30000$ per month and owning exactly $2$ vehicles.
$ii.$ Earning $₹ 40000$ or more per month and owning exactly $1$ vehicle.
$iii.$ Earning less than $₹ 25000$ per month and not owning any vehicle.
$iv.$ Earning $₹ 35000 - ₹ 40000$ per month and owning $ 2$ or more vehicles.
$v.$ Owning not more than $1$ vehicle.
Answer
$i.$ Probability that a family chosen is earning $₹ 25000 - ₹ 30000$ per month and owning exactly $2$ vehicles $=\frac{27}{2400}=\frac{9}{800}$
$ii.$ Probability that a family chosen is Earning $₹ 40000$ or more per month and owning exactly $1$ vehicle $=\frac{579}{2400}=\frac{193}{800}$
$iii.$ Probability that a family chosen is earning less than $₹ 25000$ per month and not owning any vehicle $=\frac{10}{2400}=\frac{1}{240}$
$iv.$ 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$)$
$=\frac{59+25}{2400}$
$=\frac{84}{2400}$
$=\frac{7}{200}$
$v.$ Probability that a family chosen is owning not more than $1$ vehicle $=$ Probability$($Families owning $0$ vehicle $+$ Families owning $1$ vehicle$)$
$=\frac{(10+0+1+2+1)+(160+305+535+469+579)}{2400}$
$=\frac{14+2048}{2400}$
$=\frac{2062}{2400}$
$=\frac{1031}{1200}$
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Question 35 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:
$i. 30$ years or more but less than $40$ years$?$
$ii. 50$ years or more but less than $70$ years$?$
$iii.10$ years or more but less than $40$ years$?$
$iv. 10$ years or more$?$
$v.$ Less than $10$ years$?$
Answer
Total number of patients $= 360$
$i.$ Probability that the age selected patients is $30$ years or more but less than $40$ years $=\frac{60}{360}=\frac{1}{6}$
$ii.$ Probability that the age selected patients is $50$ years or more but less than $70$ years $=\frac{50+30}{360}=\frac{80}{360}=\frac{2}{9}$
$iii.$ Probability that the age selected patients is $10$ years or more but less than $40$ years $=\frac{90+50+60}{360}=\frac{200}{360}=\frac{5}{9}$
$iv.$ Probability that the age selected patients is $10$ years or more$=1$
$v.$ Probability that the age selected patients is less than $10$ years $=0$
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