7.1 Probability of an Event

7.1 Probability of an Event

The probability of an event A, P(A) is given by

\begin{array}{l} P (A) = \frac{Number of times event A occurs}{Number of trials} \\ P (A) = \frac{n (A)}{n (S)} \\ where 0 \leq P (A) \leq 1 \end{array}

If P(A) = 0, then the event A will certainly not occur.

If P(A) = 1, then the event A is sure to occur.

Example 1:

A box contains 9 red pens and 13 blue pens. Tom puts another 4 red pens and 2 blue pens into the box. A pen is picked at random from the box. What is the probability that a red pen is picked?

Solution:

n(S) = 9 + 13 + 4 + 2 = 28

Let A = Event that a red pen is picked

n(A) = 9 + 4 = 13

\begin{array}{l} P (A) = \frac{n (A)}{n (S)} \\ = \frac{13}{28} \end{array}

Example 2:

A bag contains 45 green cards and yellow cards. A card is picked at random from the bag. The probability that a green card is picked is

\frac{1}{5} .

How many green cards must be added to the bag so that the probability of picking a green card becomes ½?

Solution:

n(S) = 45

Let

x = number of green cards in the bag.

A = Event of randomly picking a green card.

n(A) = x

\begin{array}{l} P (A) = \frac{n (A)}{n (S)} \\ \frac{1}{5} = \frac{x}{45} \\ x = \frac{45}{5} \\ x = 9 \end{array}

Let y is the number of green cards added to the bag.

\frac{9 + y}{45 + y} = \frac{1}{2}

2 (9 + y) = 45 + y

18 + 2y= 45 + y

2y – y = 45 – 18

y = 27