StudentAidUnit 13: Probability — Exercise 13 2
9th Class Mathematics · Unit 13: Probability
13.2.1.A researcher collected data on number of deaths from Horse-Ricks in Russian Army crops over to years. The table is as follows: No. of death: 0,1,2,3,4,5,6; Frequency: 60,50,87,40,32,15,10. Find the relative frequency of the given data.
Formula
Relative frequency
r.f. = fSigma f
Total
Sigma f = 60+50+87+40+32+15+10 = 294
Result
No. of death = 0
60294 = 1049
No. of death = 1
50294 = 25147
No. of death = 2
87294 = 2998
No. of death = 3
40294 = 20147
No. of death = 4
32294 = 16147
No. of death = 5
15294 = 598
No. of death = 6
10294 = 5147
13.2.2.The frequency of defective products in 750 samples are shown in the following table. No. of defectives per sample: 0,1,2,3,4,5,6,7,8; No. of sample: 120,140,94,85,105,50,40,66,50. Find the relative frequency for the given table.
Formula
Relative frequency
r.f. = fSigma f
Total
Sigma f = 120+140+94+85+105+50+40+66+50 = 750
Result
0 defectives
120750 = 425
1 defective
140750 = 1475
2 defectives
94750 = 47375
3 defectives
85750 = 17150
4 defectives
105750 = 21150
5 defectives
50750 = 115
6 defectives
40750 = 475
7 defectives
66750 = 33375
8 defectives
50750 = 115
13.2.3.A quiz competition on general knowledge is conducted. The number of corrected answers out of 5 questions for 100 sets of questions is given below. X: 0,1,2,3,4,5; f: 10,23,15,25,18,9. Find the relative frequencies for the given data.
Formula
Relative frequency
r.f. = fSigma f
Total
Sigma f = 10+23+15+25+18+9 = 100
Result
X=0
10100 = 110
X=1
23100
X=2
15100 = 320
X=3
25100 = 14
X=4
18100 = 950
X=5
9100
13.2.4.A survey was conducted from the 50 students of a class and asked about their favourite food. The responses are as under: Biryani 40, Fresh Juice 07, Chicken 21, Bar.B.Q 15, Sweets 25. (i) how many percentages of students like biryani? (ii) how many percentages of students like chicken? (iii) which food is the least like by the students? (iv) which food is the most prefer by the students?
Given
Total students
n(S) = 50
Result
(i) Biryani
4050 = 0.8 = 80%
(ii) Chicken
2150 = 0.42 = 42%
(iii)
Fresh Juice is the least liked (7 out of 50)
(iv)
Biryani is the most preferred (40 out of 50)
13.2.5.In 500 trials of a thrown of two dice, what is expected frequency that the sum will be greater than 8?
Given
Sample space
S = {(1,1),ldots,(6,6)} ; n(S) = 36
Event: sum > 8
A = {(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)} ; n(A) = 10
Working
P(A) = n(A)n(S) = 1036 = 518
Formula
Expected frequency
E(A) = N × P(A)
Working
= 500 × 518 = 138.89
Result
≈ 139
13.2.6.What is the expectation of a person who is to get Rs. 120 if he obtains at least 2 heads in single toss of three coins?
Given
Sample space
S = {HHH,HTH,HHT,THH,TTH,THT,HTT,TTT} ; n(S) = 8
Event: at least 2 heads
A = {HHH,HTH,HHT,THH} ; n(A) = 4
Working
P(A) = n(A)n(S) = 48 = 12
Formula
Expected frequency
E(A) = N × P(A)
Result
= 120 × 12 = 60
13.2.7.Find the expected frequencies of the given data if the experiment is repeated 200 times. x: 0,1,2,3,4,5,6; P(x): 0.11,0.21,0.17,0.18,0.09,0.17,0.07.
Formula
Expected frequency
EF = P(X) × 200
Result
X=0
0.11 × 200 = 22
X=1
0.21 × 200 = 42
X=2
0.17 × 200 = 34
X=3
0.18 × 200 = 36
X=4
0.09 × 200 = 18
X=5
0.17 × 200 = 34
X=6
0.07 × 200 = 14
13.2.8.The probability of getting 5 sixes while tossing six dice is 2/5. How many times would you expect it to show 5 sixes?
Given
N = 200 ; P(A) = 25
Formula
Expected frequency
E(A) = N × P(A)
Result
= 200 × 25 = 80 times