If the odds in favour of an event be 3-3- find the probability of the occurrence of the event-

Let the given event be E and let P(E) = x. Then, odds in favour of E =P(E)/1 P(E) ⇔P(E)/1 P(E)=3/5⇔x/(1 x) = 3/5 ⇔ 5x=3 3x ⇔ 8x=3 ⇔ x=3/8 ∴ Required probability ...

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Standard XI

Mathematics

Mutually Exclusive Events

If the odds i...

Question

If the odds in favour of an event be $\frac{3}{3}$ , find the probability of the occurrence of the event.

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Solution

Let the given event be E and let $P (E) = x$ . Then,

odds in favour of E $= \frac{P (E)}{1 - P (E)}$

$\Leftrightarrow \frac{P (E)}{1 - P (E)} = \frac{3}{5} \Leftrightarrow \frac{x}{(1 - x)} = \frac{3}{5}$

$\Leftrightarrow 5 x = 3 - 3 x \Leftrightarrow 8 x = 3 \Leftrightarrow x = \frac{3}{8}$

$∴$ Required probability $= \frac{3}{8}$

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If the odds in favour of an event be 33, find the probability of the occurrence of the event.

Let the given event be E and let P(E)=x. Then, odds in favour of E =P(E)1−P(E) ⇔P(E)1−P(E)=35⇔x(1−x)=35 ⇔5x=3−3x⇔8x=3⇔x=38 ∴ Required probability =38

If the odds in favour of an event be $\frac{3}{3}$ , find the probability of the occurrence of the event.