RS Aggarwal 2019,2020 solution class 7 chapter 23 Probability Exercise 23

Exercise 23

Page-283

Question 1:

A coin is tossed 300 times and we get head : 136 times and tail : 164 times.
When a coin is tossed at random, What is the probability of getting (i) a head, (ii) a tail?

Answer 1:

Total number of trials = 300
Number of times a head is obtained = 136
Number of times a tail is obtained= 164

(i) Probability of getting head =$\frac{\mathrm{Numbe}r \mathrm{of} \mathrm{times} \mathrm{heads} \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials}}$=$\frac{136}{300}=\frac{34}{75}$

(ii) Probability of getting a tail =$\frac{\mathrm{Number} \mathrm{of} \mathrm{times} \mathrm{tails} \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials}}$=$\frac{164}{300}=\frac{41}{75}$

Question 2:

Two coins are tossed simultaneously 200 times and we get two heads: 58 times, one head: 83 times: 0 head: 59 times.
When two coins are tossed at random, what is the probability of getting (i) 2 heads, (ii) 1 head, (iii) 0 head?

Answer 2:

Total number of trials = 200
Number of times 2 heads are obtained = 58
Number of times one head is obtained  = 83
Number of times no head is obtained = 59

(i) Probability of getting 2 heads =  $\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 2 \mathrm{heads} \mathrm{have} \mathrm{been} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }$ = $\frac{58}{200}=\frac{29}{100}$


(ii) Probability of getting 1 head = $\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 1 \mathrm{head} \mathrm{has} \mathrm{been} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }$ = $\frac{83}{200}$


(iii) Probability of getting 0 head =  $\frac{\mathrm{Number} \mathrm{of} \mathrm{times} \mathrm{head} \mathrm{has} \mathrm{not} \mathrm{been} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }$ = $\frac{59}{200}$

Question 3:

A dice is thrown 100 times and the outcomes are noted as given below:

Outcome	1	2	3	4	5	6
Frequency	21	14	18	15	23	9

When a dice is thrown at random, what is the probability of getting a (i) 3, (ii) 6, (iii) 6, (iv) 1?

Answer 3:

Total number of trials = 100
Number of times 3 is obtained = 18
Number of times 6 is obtained = 9
Number of times 4 is obtained = 15
Number of times 1 is obtained =  21

$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{Probability} \mathrm{of} \mathrm{getting} \mathrm{a} 3=\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 3 \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }=\frac{18}{100}=\frac{9}{50} \\ \left(\mathrm{ii}\right) \mathrm{Probability} \mathrm{of} \mathrm{getting} \mathrm{a} 6=\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 6 \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }=\frac{9}{100} \\ \left(\mathrm{iii}\right) \mathrm{Probability} \mathrm{of} \mathrm{getting} \mathrm{a} 4=\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 4 \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }=\frac{15}{100}=\frac{3}{20} \\ \left(\mathrm{iv}\right) \mathrm{Probability} \mathrm{of} \mathrm{getting} \mathrm{a} 1=\frac{\mathrm{Number} \mathrm{of} \mathrm{times} 1 \mathrm{is} \mathrm{obtained}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{trials} }=\frac{21}{100} \end{gathered}$$

Question 4:

In a survey of 100 ladies it was found that 36 like coffee while 64 dislike it.
Out of these ladies, one is chosen at random. What is the probability that the chosen lady (i) likes coffee, (ii) dislikes coffee?

Answer 4:

Total number of ladies surveyed = 100
Ladies who like coffee = 36
Ladies who do not like coffee = 64

$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{Probability} \mathrm{of} \mathrm{choosing} \mathrm{a} \mathrm{lady} \mathrm{who} \mathrm{likes} \mathrm{coffee}=\frac{\mathrm{Number} \mathrm{of} \mathrm{ladies} \mathrm{who} \mathrm{like} \mathrm{coffee}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{ladies} }=\frac{36}{100}=\frac{9}{25} \\ \left(\mathrm{ii}\right) \mathrm{Probability} \mathrm{of} \mathrm{choosing} \mathrm{a} \mathrm{lady} \mathrm{who} \mathrm{dislikes} \mathrm{coffee}=\frac{\mathrm{Number} \mathrm{of} \mathrm{ladies} \mathrm{who} \mathrm{dislike} \mathrm{coffee}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{ladies} }=\frac{64}{100}=\frac{16}{25} \end{gathered}$$