मराठी

One of the Two Events Must Happen. Given that the Chance of One is Two-third of the Other, Find the Odds in Favour of the Other. - Mathematics

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प्रश्न

One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.

उत्तर

Let the given events be A and B
Now,

\[P\left( A \right) = \frac{2}{3}P\left( B \right)\]
Let P(B) = x
\[\therefore P\left( A \right) = \frac{2}{3}x\]
The events A and B are exhaustive.
∴ P(A) or P(B) = 1
⇒ P(A) + P(B) = 1                (∵ A and B are mutually exclusive)
 \[\Rightarrow \frac{2}{3}x + x = 1\]
\[\Rightarrow \frac{5x}{3} = 1\]
\[\Rightarrow x = \frac{3}{5}\]
\[\therefore P\left( B \right) = \frac{3}{5}\]

This implies that the odds in favour of B are 3 : (5 – 2), i.e. 3 : 2.

 
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Probability - Probability of 'Not', 'And' and 'Or' Events
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पाठ 33: Probability - Exercise 33.4 [पृष्ठ ६८]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 33 Probability
Exercise 33.4 | Q 7 | पृष्ठ ६८

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