Mathematics Lab Activity-14 Class XII

Mathematics Laboratory Activities 12 on Probability for class XI Non-Medical students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 13 : Probability

Activity - 14

Objective

To explain the computation of conditional probability of a given event A, when event B has already occurred, through an example of throwing a pair of dice.

Material Required

A piece of plywood, white paper, pen/pencil, scale, a pair of dice

Procedure

1. Paste a white paper on a piece of plywood of a convenient size.

2. Make a square  and divide it into 36 unit squares of size 1 cm each as shown in figure 14.1.

3. Write pair of numbers as shown in the figure.

Figure 14.1

4. Figure 14.1  gives all possible outcomes of the given experiment of tossing a pair of dice once. Hence, it represents the sample space of the experiment.

5. Suppose we have to find the conditional probability of an event A if an event B has already occurred, where 

   Event A = Number 4 appears on both the dice and 

   Event B = Number 4 has appeared on at least one of the dice

6. It means we have to find the probability of event A with condition of event B  i.e. P(A|B).

Observations

1. No. of outcomes favorable to event A = "1" (4, 4)
⇒ n(A) = 1
⇒ P(A) = 1/36

2. No. of outcomes favorable to event B = "11"
(1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6)
⇒ n(B) = 11
⇒ P(B) = 11/36

3. No. of outcomes favorable to A ⋂ B = "1" (4, 4)
⇒ n(A ⋂ B) = 1
⇒ P(A ⋂ B) = 1/36

4. Now probability of A with condition of B is given by
P(A|B) = P(A ⋂ B)/P(B) 

Result

We have explained the method of finding conditional probability of and event.

Applications

This activity is helpful in understanding the concept of conditional probability which further helpful in Baye’s Theorem.

VIVA – VOICE

Q1. What are mutually exclusive events ?

Ans. A set of events is said to be mutually exclusive if the happening of one excludes the happening of the other.

Q2. What are exhaustive events ?

Ans. A set of events is said to be exhaustive if the performance of the experiment always result in the occurrence of atleast one of them.

Q3. What is conditional probability ?

Ans. The probability of even B when the event A has already occured is called the conditional probability of B and is denoted by P(B/A).

Q4. What is the union of two mutually exclusive and exhaustive events A and B ?

Ans. AሀB = S

Q5. What is the intersection of two mutually exclusive events A and B ?

AกB = ф

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