Question

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Answer 1

Question:

A is an event of a random experiment , such that ; P(A) : P(A') = 1 : 2 , find the value of P(A') .

Answer:

P(A') = 2/3

Note:

• Experiment : It is an operation which can produce some well defined outcomes .

• There are two types of experiments :-

1) Deterministic experiment

2) Random (or probability) experiment

• Deterministic experiment : An experiment whose output (or result) is fixed (or known) is called a deterministic experiment .

• Probability of deterministic experiment is always one, ie; P(E) = 1 .

• Random experiment : An experiment whose outcomes cannot be predicted with certainty is called a random experiment.

• Probability of random experiment varies between 0 to 1, ie; 0 ≤ P(E) ≤ 1 .

• Sample space : the set of all possible outcome of a random experiment is called the sample space for that experiment. It is usually denoted by S.

• Sample point or Event point : Each element of the sample space is called sample point or even point .

• Mathematical or Classical definition of Probability : If S is the sample space then probability of occurrence of an event E is denoted by P(E) and is defined as ;

P(E) = n(E)/n(S)

P(E) $= \frac{no. \: of \: elements \: in \: E}{no. \: of \: elements \: in \: S}$

P(E) $= \frac{total \: no. \: of \: favourable \: outomes}{total \: no. \: of \: sample \: points}$

• Probability of occurrence of an event always lies between 0 and 1 .

ie; 0 ≤ P(E) ≤ 1 .

• Complement of an event : If S is the sample space for a random experiment and E is an event , then ;

• Complement of the event E is denoted by E' or E° or Ē .

• E' means non occurrence of event E .

• E' occurs if and only if E doesn't occur.

• The probability of non occurrence of an event E is denoted by P(E') .

• Also , If E is an event and E' is the complement of event E , then ;

P(E) + P(E') = 1 .

Solution:

Here,

It is given that ;

For an event A , P(A) : P(A') = 1 : 2 .

Thus,

Let P(A) = x and P(A') = 2x

Also,

We know that ;

=> P(A) + P(A') = 1

=> x + 2x = 1

=> 3x = 1

=> x = 1/3

Thus,

P(A) = x = 1/3

P(A') = 2x = 2•(1/3) = 2/3

Hence,

The required value of P(A') is 2/3 .