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Chapter 11: Problem 43

A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and the other is not burned on either side. You are served one of the pancakes at random, and the side facing you is burned. What is the probability that the other side is burned? (Hint: Use conditional probability.)

Short Answer

Expert verified
The probability that the pancake is burned on the other side given that one side is burned is approximately 0.75.

Step by step solution

01

Define Events

First define two events. Let A be the event 'Pancake is burned on both sides' and B be the event 'Pancake is burned on the side facing up.' There are 3 pancakes, thus there are six sides in total. Among them, four sides are burned.
02

Calculate the Probabilities

We calculate the probabilities of the two events. The probability that a random pancake is burned on both sides (Event A) is 1 out of 3, \( P(A) = 1/3 = 0.33 \). The probability that a random side of a pancake is burned (Event B) is 4 out of 6, \( P(B) = 4/6 = 0.67 \). The probability that a pancake is burned on both sides given that one side is burned (Event A intersects event B) is 2 out of 4, since for the pancake burned on both sides, both sides are burned. \( P(A \cap B) = 2/4 = 0.5 \).
03

Use the Formula for Conditional Probability

The conditional probability of event A given event B is given as \( P(A | B) = P(A \cap B) / P(B) \).
04

Calculate the Seeked Probability

Substitute the probabilities calculated in step 2, \( P(A | B) = 0.5 / 0.67 \approx 0.75 \).

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