Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 or 7?

n(S) = 36
n(E) = {(5,6), (6,5)} = 2
? p(E) = n(E) / n(S) = 2/36 = 1/18

n(S) = 6, n(E) = (4, 6) = 2
? P(E) = 2/6 = 1/3

Total number of cards n(S) = 52
Number of red cards n(E) = 26
? P(E) = n(E)/n(S) = 26/52 = 1/2

Total number of letters = n(S) = 11
whereas, number of vowels = n(E) = 4
? Required probability = n(E)/n(s) = 4/11

Required probability = P(A) x P(B)
= (7/8) x (9/10)
= 63/80

Number of cases favourable of E = 4
Total Number of cases = (5 + 4 ) = 9
? P(E) = 4/9

n(S) = Number of ways of drawing 2 balls out of 13 = ¹³C₂ = 13 x 12 / 2= 78
n(E) = No. of ways of drawing 2 balls out of 5 = ⁵C₂ = 5 x 4 / 2 = 10

? P(E) = n(E)/n(S) = 10/78 = 5/39

Total no. of balls = (6 + 8) = 14
No. of white balls = 8
? P(drawing a white ball) = 8/14 = 4/7

? n(S) = (2)³ = 8
E = Event of getting 0, or 1 or 2 heads
= {TTT, TTH, THT, HTT, HHT, HTH, THH}
? n(E) = 7
? P(E) = n(E)/n(S) = 7/8

S= { HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} and
E = Event of getting exactly two heads = {HHT, HTH, THH}
? P(E) = n(E)/n(S) = 3/8