If C and D are two events such that C D and P(D) ≠ 0, then the correct statement among the following is [AIEEE 2011]

Correct Answer is : P(CD)≥P(C)P ≤ft( C/D ) ≥ P(C)P(DC)≥P(C)

Correct Answer is : P(CD)≥P(C)P ≤ft( C/D ) ≥ P(C)P(DC)≥P(C)

Test Index

Probability Part 1

Section: Mathematics

Question : 80 of 100

Marks: +1, -0

C

D

C \subset D

P(D) \neq 0

Solution:

Given that

C \subset D

means

C

is present entirely inside

D

. Which is shown below.

P \left( \frac{C}{D} \right) = \frac{P(C \cap D)}{P(D)} = \frac{P(C)}{P(D)}

C \cap D

means common part of events

C

and

D

which is equal to

C

\;0 \leq P(D) \leq 1

\; \therefore \; \frac{P(C)}{P(D)} \geq P(C)

Note: Here we are dividing with

P(D)

which is

\leq 1

and

\geq 0

, as we know on dividing with a number

n

in the range

0 \leq n \leq 1

we get always more than or equal to the original number.

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