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A number x is chosen at random from the set ${1, 2, 3, ..........., 15} .$ If E denotes the event that $\sin (x^{c})$ is positive, then the odds in favor of E is_________ $(x^{c} m e a n s x r a d i a n s)$

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$3 : 5$

$5 : 3$

$2 : 3$

$3 : 2$

answer is C.

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Detailed Solution

$n (S) = 15 \sin (x^{c}) > 0 \Rightarrow x \in (0, π) o r (2 π, 3 π) o r (4 π, 5 π) a n d π ≃ 3.14 ∴ x = 1, 2, 3, 7, 8, 9, 13, 14, 15 a r e f a v o u r b l e t o E P (E) = \frac{9}{15} = \frac{3}{5} a n d P (E) : P (\bar{E}) = 3 : 2$

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