RS Aggarwal Solutions: Probability- 3 | RS Aggarwal Solutions for Class 10 Mathematics PDF Download

The probability of any event is always positive. It could be at the least equal to zero but not less than that. The probability of sure event at the maximum could be equal to 1 so probability lies between 0 and 1 both included.

Probability of event P + probability of event not P = 1
P (non –happening of event P) = (1-P)

The probability of impossible event is always zero because such event can never happen.

The probability of sure event or event which is certain to happen is always 1.

The probability of event is always less than or equal to 1. 1.5 being greater than 1 can never be the probability of an event.

Let E be the event of selecting a prime number
Total numbers of elementary events are 30
Favourable numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Number of favourable outcome = 10
P (E) = 10/30 =1/3

Total numbers of elementary event are 15
Let E be the event of selecting a multiple of 4
Favourable outcomes are: 4, 8, 12,
Numbers of favourable outcomes are 3
P (E) = 3/15 = 1/5

Total numbers of elementary events are: 50 – 5 = 45 number 6 is included
Let E be the event of drawing a perfect square
The favourable outcomes are: 9, 16, 25, 36, 49
Numbers of favourable outcomes = 5
P (E) = 5/45 = 1/9

Total numbers of elementary events are: 90
Let E be the event of getting a prime number less than 23
Favourable numbers are: 2, 3, 5, 7, 11, 13, 17, 19
Numbers of favourable outcomes = 8
P (E) = 8/90 = 4/45

Total numbers of elementary events are 10
Let E be the event of getting a prime number
Favourable numbers are: 2, 3, 5, 7, 11
Numbers of favourable outcomes = 5
P (E) = 5/10 =1/2

Total numbers of elementary events are: 40
Let E be the event of getting multiple of 7
Favourable outcomes are: 7, 14, 21, 28, 35
Number of favourable outcome = 5
P(E) = 5/40 = 1/8

On actual division 7/6 comes out to be 1.67 which is greater than 1. The probability can be less than or equal to 1.

Probability of winning a game + probability of losing a game = 1
So probability of losing the game = 1- probability of winning = 1 – 0.4 = 0.6

The probability of event which can not occur or impossible event is always zero

Total numbers of elementary events are: 20
Let E be the event of getting a multiple of 5
Favourable numbers are: 5, 10, 15, 20
Number of favourable events are= 4
P (E) = 4/20 = 1/5

Total numbers of elementary events are: 25
Let E be the event of getting a multiple of 3 or 5
The favourable numbers are: 3, 6, 9, 12, 15, 18, 21, 24, 5, 10, 15, 20, 25
Numbers of favourable events = 13
P (E) = 13/25

Total numbers of elementary events are 15 – 5 = 10
Let E be the event of drawing card less than 10
Favourable numbers are: 6, 7, 8, 9
Numbers of favourable outcomes = 4
P (E = 4/10 =2/5

Total numbers of elementary events are: 6
Let E be the event of getting an even number
Favourable numbers are: 2, 4, 6
Number of favourable outcomes = 3
P (E) = 3/6 = 1/2

Total numbers of elementary events are: 6
Let E be the event of getting number greater than 2
Favourable numbers are: 3, 4, 5, 6
Numbers of favourable outcomes = 4
P (E) = 4/6 = 2/3

Total numbers of elementary events are: 6
Let E be the event of getting an odd number greater than 3
Favourable number: 5
Number of favourable outcome =1
P (E) = 1/6

Total numbers of elementary events are: 6
Let E be the event of getting a prime number
Favourable numbers are: 2, 3, 5
Numbers of favourable outcomes are = 3
As we know,

P (E) = 3/6
= 1/2

Total numbers of elementary events are: 6 x6 = 36
Let E be the event of getting the same number on both the dice
Favourable events are: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Numbers of favourable outcomes are: 6
P (E) = 6/36 = 1/6

Total numbers of elementary events are: 2 x 2 = 4
Let E be the event of getting 2 heads
Favourable event is HH
Number of favourable outcome = 1
P (E) = 1/4

Total numbers of elementary events are: 6 x 6 = 36
Let E be the event of getting a doublet
Favourable outcomes are: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Number of favourable outcomes = 6

P (E) = 6/36
=1/6

Total numbers of elementary events are: 2 x 2 = 4
Let E be the event of getting at most one head
Note: atmost one head means one head or no head at all, outcomes are considerable
Favourable events are: TT, HT, TH
Numbers of favourable outcomes = 3
P (E) = 3/4

Total numbers of elementary events are: 2 x 2 x 2 = 8
Let E be the event of getting exactly two head
Favourable outcomes are: HHT, THH, HTH
Numbers of favourable outcomes = 3
P (E) = 3/8

Total numbers of elementary events are : 24
Let E be the event of getting a prize
Favourable outcomes = 8
P (E) = 8/24 = 1/3

Total numbers of elementary events are: 30
Let E be the probability of not getting a prize
Numbers of Favourable outcomes= 24
P (E) = 24/30 = 12 /15 = 4/ 5

Total numbers of elementary events are: 3 + 2 + 4 = 9
Let E be the event of not white ball drawn
Numbers of non-favourable outcomes = numbers of white ball drawn = 2
P (white ball) = 2/9
P (E) = 1- 2/9 = 7/9

Total numbers of elementary events are: 4 + 6 = 10
Let E be the event of drawing black ball
Numbers of favourable events are: 6
P (E) = 6/10 = 3/5

Total numbers of elementary events are: 8 + 2 + 5 = 15
Let E be the event of drawing not black ball
Number of non-favourable events = numbers of outcome with white ball drawn = 2/15
P(non- black drawn) = 1 – 2/15 = 13/15

Total numbers of elementary events are: 3 + 4 + 5 = 12
Let E be the event of drawing neither black ball nor white ball
Number of outcomes of drawing a black ball or white ball = 5/ 12 + 3/12 = 8/12 = 2/3
Number of favourable outcomes are = 1-2/3 = 1/3

Total numbers of elementary events are: 52
Let E be the event of drawing black king
Favourable outcomes are: 2
P (E) = 2/52 = 1/26

Total numbers of elementary events are: 52
Let E be the event of getting a queen
Numbers of Favourable outcomes are : 4
P (E) = 4/52 = 2/ 26 = 1/13

Total numbers of elementary events are: 52
Let E be the event of drawing face card
Favourable events are: 4 cards of jack, 4 cards of queen and 4 cards of king
Number of favourable events = 12
P (E) = 12/ 52 = 6/26 = 3/13

Total numbers of elementary events are: 52
Let E be the event of drawing black face card
Favourable events are: 2 black face cards of jack, 2 black face cards of queen and 2 black face cards of king = 6
P (E) = 6/52 = 3/ 26

Total numbers of elementary events are: 52
Let E be the event of getting a ‘6’ number card
Numbers of Favourable events are: 4
P (E) = 4/52 = 1/13