Let a fair coin is tossed 3 times and E,F,G be events 'getting a head in the first toss', 'getting an odd no. of tails' and 'getting at least one head and at least one tail' respectively. Consider the following statements
Statement 1: Events E,F,G are pairwise independent.
Statement 2: Events E,F,G are independent

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Statement 1 is true, statement 2 is true, statement 2 is a correct explanation of statement 1

Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation of statement 1.

Statement 1 is false, statement 2 is true.

Statement 1 is true, statement 2 is false

answer is C.

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Detailed Solution

$P (E) = \frac{4}{8}, P (F) = \frac{4}{8}, P (G) = \frac{6}{8} P (E \cap F) = \frac{2}{8}, P (F \cap G) = \frac{3}{8}, P (G \cap E) = \frac{3}{8} P (E \cap F \cap G) = \frac{2}{8}$

So, $P (E \cap F) = P (E) P (F), P (F \cap G) = P (F) P (G),$

$P (G \cap E) = P (G) P (E) b u t P (E \cap F \cap G) \neq P (E) P (F) P (G)$

$∴ E, F, G$ are pairwise independent only

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