Probability is the number of outcomes of an event (possible outcomes) divided by the number of outcomes. The probability of an event (x) occurring is denoted as P(x)

P(x) = number of occurance of an event (x)total of outcomes

Ex: a) Given the following numbers 2, 1, 4, 6, 8, 9, 4. Find the probability that a number chosen randomly from the group will be 4.

b) A bag contains 45 balls. Among these 12 are green, 13 are blue and 18 are yellow. Find the probability that a ball chosen at a random will be a blue ball, a yellow ball, a green ball, neither yellow nor green

Solution:

a) Total number of 4s = 2

Total number of elements = 7

P (4) = total number of 4stotal number of elements = 2/7

b)  Total number of balls = 45

Number of blue balls = 15

P(blue balls) = 15/45 = 1/3

Number of yellow balls = 18

P(yellow balls) = 18/45 = 2/5

Number of green balls = 12

P(green balls) = 12/45 = 4/15

Having neither a green ball nor a green ball is another way of saying having a blue ball, since the bag has only 3 colours.

P(neither yellow nor green balls) = P(blue) = 1/3

NB: P(blue) + P(yellow) + P(green) = 1/3 + 2/5 + 4/15 = 1*5+3*2+(1*4)15 = 15/15 = 1

Therefore, the sum of the probability of all events occurring together is 1