StudentAidUnit 13: Probability — Review Exercise
9th Class Mathematics · Unit 13: Probability
R13.3.An urn contains 10 red balls, 5 green balls and 8 blue balls. Find the probability of selecting at random. (i) a green ball (ii) a red ball (iii) a blue ball (iv) not a red ball (v) not a green ball
Given
Sample space
n(S) = 10+5+8 = 23
Result
(i) Green
P(A) = 523
(ii) Red
P(A) = 1023
(iii) Blue
P(A) = 823
(iv) Not red
P(A') = 1 - 1023 = 1323
(v) Not green
P(A') = 1 - 523 = 1823
R13.4.Three coins are tossed together. what is the probability of getting: (i) exactly three heads (ii) at least two tails (iii) not at least two heads (iv) not exactly two heads
Given
Sample space
S = {HHH,HTH,HHT,THH,TTH,THT,HTT,TTT} ; n(S) = 8
Result
(i)
A = {HHH} ; n(A)=1 ⇒ P(A) = 18
(ii)
A = {TTH,THT,HTT,TTT} ; n(A)=4 ⇒ P(A) = 48 = 12
Given
(iii)
A = {HHH,HTH,HHT,THH} ; n(A)=4 ⇒ P(A) = 48 = 12
(iii)
P(A') = 1 - 12 = 12
(iv)
A = {HTH,HHT,THH} ; n(A)=3 ⇒ P(A) = 38
(iv)
P(A') = 1 - 38 = 58
R13.5.A card is drawn from a well shuffled pack of 52 playing cards. What will be the probability of getting: (i) king or jack of red colour (ii) not "2" of club and spade
Given
Sample space
n(S) = 52
Result
(i)
n(A) = 2+2 = 4 ⇒ P(A) = 452 = 113
Given
(ii)
A = {2 of club, 2 of spade} ; n(A)=2 ⇒ P(A) = 252 = 126
P(A') = 1 - 126 = 2526
R13.6.Six coins are tossed 600 times. The number of occurrence of tails are recorded and shown in the table given below: No. of tails: 0,1,2,3,4,5,6; Frequency: 110,90,105,80,76,123,16. Find the relative frequency of given table.
Formula
Relative frequency
r.f. = fSigma f
Total
Sigma f = 110+90+105+80+76+123+16 = 600
Result
0 tails
110600 = 1160
1 tail
90600 = 320
2 tails
105600 = 740
3 tails
80600 = 215
4 tails
76600 = 19150
5 tails
123600 = 41200
6 tails
16600 = 275
R13.7.From a lot containing 25 items, 8 items are defective. Find the relative frequency of non-defective items, also find the expected frequency of non-defective items.
Given
Total items = 25 ; Defective items = 8
Non-defective items
25 - 8 = 17
Result
Expected frequency of non-defective
17
Formula
Relative frequency
R.F. = frac{frequency of non-defective items{total items
Result
1725 = 0.68