The price of petrol rises in 80 % of the cases and the price of diesel

1.	The price of petrol rises in 80 % of the cases and the price of diesel rises in 77% of the cases after the rise in price of crude oil. The price of petrol and diesel rises in 68 % cases. Find the probability that the price of diesel rises under the condition that there is a rise in the price of petrol.
Answer» A = Event that the price of petrol rises ∴ P(A) = \(\frac{80}{100}\) B = Event that the price of diesel rises ∴ P(B) = \(\frac{77}{100}\) A ∩ B = Event that the prices of both petrol and diesel rises ∴ P(A ∩ B) = \(\frac{68}{100}\) B\|A = Event that the price of diesel rises knowing that the price of petrol rises ∴ P(B\|A) = \(\frac{P(A∩B)}{P(A)}\) \(=\cfrac{\frac{68}{100}}{\frac{80}{100}}\) \(= \frac{68}{100}×\frac{100}{80}=\frac{17}{20}\)

The price of petrol rises in 80 % of the cases and the price of diesel rises in 77% of the cases after the rise in price of crude oil. The price of petrol and diesel rises in 68 % cases. Find the probability that the price of diesel rises under the condition that there is a rise in the price of petrol.

Answer»

A = Event that the price of petrol rises

∴ P(A) = \(\frac{80}{100}\)

B = Event that the price of diesel rises

∴ P(B) = \(\frac{77}{100}\)

A ∩ B = Event that the prices of both petrol and diesel rises

∴ P(A ∩ B) = \(\frac{68}{100}\)

B|A = Event that the price of diesel rises knowing that the price of petrol rises

∴ P(B|A) = \(\frac{P(A∩B)}{P(A)}\)

\(=\cfrac{\frac{68}{100}}{\frac{80}{100}}\)

\(= \frac{68}{100}×\frac{100}{80}=\frac{17}{20}\)

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