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Maths 5 Marks Questions

Data Handling IV (Probability) · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 2 questions.

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Question 15 Marks
Two coins are tossed simultaneously $500$ times and the outcomes are noted as given below:
Outcome:
Two heads $(HH)$
One head $(HT$ or $TH)$
No head $(TT)$
Frequency:
$105$
$275$
$120$
If same pair of coins is tossed at random, find the probability of getting:
$i.$ Two heads
$ii.$ One head
$iii.$ No head
Answer
Number of trials $= 500$ Number of outcomes of two heads $(HH) = 105$
Number of outcomes of one head $(HT$ or $TH) = 275$
Number of outcomes of no head $(TT) = 120$
$i.$ Probability of getting two heads $=\frac{\text{Frequency of getting 2 heads}}{\text{Total No. of trails}}=\frac{105}{500}=\frac{21}{100}$
$ii.$ Probability of getting one heads $=\frac{\text{Frequency of getting 1 heads}}{\text{Total No. of trails}}=\frac{275}{500}=\frac{11}{20}$
$iii.$ Probability of getting no head $=\frac{\text{Frequency of getting no heads}}{\text{Total No. of trails}}=\frac{120}{500}=\frac{6}{25}$
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Question 25 Marks
A die is thrown $100$ times and outcomes are noted as given below:
Outcome:
$1$
$2$
$3$
$4$
$5$
$6$
Frequency:
$21$
$9$
$14$
$23$
$18$
$15$
If a die is thrown at random, find the probability of getting $a/ an:$
$i. 3$
$ii. 5$
$iii. 4$
$iv.$ Even number
$v.$ Odd number
$vi.$ Number less than $3$
Answer
Total number of trials $= 100$ Number of times $“1”$ comes up $= 21$ Number of times $“2”$ comes up $= 9$ Number of times $“3”$ comes up $= 14$ Number of times $“4”$ comes up $= 23$ Number of times $“5”$ comes up $= 18$ Number of times $“6”$ comes up $= 15$
$i.$ Probability of getting $3=\frac{\text{Frequency of 3}}{\text{Total No. of trails}}=\frac{14}{100}=0.14$
$ii.$ Probability of getting $5=\frac{\text{Frequency of 5}}{\text{Total No. of trails}}=\frac{18}{100}=0.18$
$iii.$ Probability of getting $4=\frac{\text{Frequency of 4}}{\text{Total No. of trails}}=\frac{23}{100}=0.23$
$iv.$ Frequency of getting an even no. $=$ Frequency of $2 +$ Frequency of $4 +$ Frequency of $6 = 9 + 23 + 15 = 47$
Probability of getting an even no. $=\frac{\text{Frequency of even number}}{\text{Total No. of trails}}=\frac{47}{100}=0.47$
$v.$ Frequency of getting an odd no. $=$ Frequency of $1 +$ Frequency of $3 +$ Frequency of $5 = 21 + 14 + 18 = 53$
Probability of getting an odd no. $=\frac{\text{Frequency of odd number}}{\text{Total No. of trails}}=\frac{53}{100}=0.53$
$vi.$ Frequency of getting a no. less than $3 =$ Frequency of $1 +$ Frequency of $2 = 21 + 9 = 30$
Probability of getting a no. less than $3 =\frac{\text{Frequency of number less than 3}}{\text{Total No. of trails}}=\frac{30}{100}=0.30$
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