Algebra

Probability

Medium

core

If E and F are independent events associated with an experiment, then which one of the following statements is correct?

$P(E \cap F) = 0$

$P(E \cup F) = 1$

$P(E|F) = P(E)$

$P(E|F) = P(F)$

✅ Correct Option: 3

For independent events E and F, one event happening doesn't affect the probability of the other event happening.

The fundamental property of independent events is:

$P(E \cap F) = P(E) \times P(F)$

The probability of both events occurring together equals the product of their individual probabilities.

Using the conditional probability formula:

$P(E|F) = \frac{P(E \cap F)}{P(F)}$

Substituting the independence property:

$P(E|F) = \frac{P(E) \times P(F)}{P(F)}$

$P(E|F) = P(E)$

This shows that even after F occurs, the probability of E remains unchanged, which is the definition of independence.

Option 1: $P(E \cap F) = 0$ would mean E and F are mutually exclusive, not independent.

Option 2: $P(E \cup F) = 1$ would mean E or F always occurs, which independence doesn't guarantee.

Option 4: $P(E|F) = P(F)$ is incorrect as $P(E|F)$ relates to event E, not event F.

The correct statement is Option 3: $P(E|F) = P(E)$

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If E and F are independent events associated with an experiment, then which one of the following statements is correct?

Solution

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