A bag contains 6 black balls and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

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

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

Clearly, n(S) = 20 and E = { 3, 6, 9, 12, 15, 18, 7, 14 } i.e., n(E) = 8

? P(E) = n(E)/ n(S) = 8/20 = 2/5

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

? 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

S = {HH, HT, TT, TH}
and E = {HH, HT, TH }
? P(E) = n(E)/n(S) = 3/4

Here S = {H, T}
and E = {H}
? P(E) = n(E)/n(S) = 1/2

The probability of absenting of the students in the class = 2/6 = 1/3
? The probability of missing his test = 1/5 x 1/3 = 1/15