Probability question where an object is chosen randomly out of two objects

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In summary, the friends were discussing a probability problem involving two opera singers and two newspapers. They calculated the probability of both recitals being reviewed in one newspaper, but the correct answer should have included the other newspaper as well. The correct probability is 13/60, which is the sum of the probabilities of both newspapers.
  • #1
tantrik
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Dear friends,

I am stuck at the following probability problem. Will appreciate your help.

Two opera singers, Mario and Clarissa both perform on the same night, in separate recitals. The independent probabilities that two newspapers X and Y publish reviews of their recitals are given below:

Probability of review in newspaper X
================================ ====
Mario's recital - 1/2
Clarissa's recital - 2/3

Probability of review in newspaper Y
================================ ====
Mario's recital - 1/4
Clarissa's recital - 2/5

Mario buys one of the newspapers at random. What is the probability that it has reviewed "both" recitals?


I did this way: P(reviewed both recitals) = P(buys paper X)*P(X reviews Mario)*P(X reviews Clarissa) = (1/2)*(1/2)*(2/3) = 1/6

But 1/6 is not the correct answer. Let me know where I am wrong and why.

Thanks in advance.
 
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  • #2
Your answer is wrong because it refers only to newspaper X! You calculated "the probability that she bought newspaper X and both were reviewed". If she had bought newspaper Y then the probability both are reviewed is (1/4)(2/5)= 1/10. The probability she bought newspaper Y was 1/2 so the probability she bought newspaper Y and both were reviewed is (1/2)(1/10)= 1/20. The probability both were reviewed in whatever paper she bought is the sum: 1/20+ 1/6= 3/60+ 10/60= 13/60.
 
  • #3
HallsofIvy said:
Your answer is wrong because it refers only to newspaper X! You calculated "the probability that she bought newspaper X and both were reviewed". If she had bought newspaper Y then the probability both are reviewed is (1/4)(2/5)= 1/10. The probability she bought newspaper Y was 1/2 so the probability she bought newspaper Y and both were reviewed is (1/2)(1/10)= 1/20. The probability both were reviewed in whatever paper she bought is the sum: 1/20+ 1/6= 3/60+ 10/60= 13/60.

Thanks for the solution. Now I understand where the mistake was.
 

FAQ: Probability question where an object is chosen randomly out of two objects

1. What is the probability of choosing one object out of two objects?

The probability of choosing one object out of two objects is 50%. This is because there are two possible outcomes (choosing one object or the other) and each outcome has an equal chance of occurring.

2. How do you calculate the probability of choosing one object out of two objects?

To calculate the probability, you divide the number of desired outcomes (choosing one specific object) by the total number of possible outcomes (choosing either object). In this case, it would be 1 desired outcome divided by 2 possible outcomes, which equals 0.5 or 50%.

3. Can the probability of choosing one object out of two objects ever be greater than 50%?

No, the probability of choosing one object out of two objects can never be greater than 50%. This is because the total number of possible outcomes is limited to two, and each outcome has an equal chance of occurring.

4. What is the difference between probability and odds in this scenario?

In this scenario, probability refers to the likelihood of choosing one object out of two objects, while odds refer to the ratio of the probability of choosing one object to the probability of not choosing that object. For example, if the probability of choosing one object is 0.5, the odds would be 0.5/0.5, which simplifies to 1.

5. How does the sample size affect the probability in this scenario?

In this scenario, the sample size does not affect the probability. This is because the probability is based on the total number of possible outcomes, not the number of times the experiment is repeated. Regardless of how many times the experiment is conducted, the probability of choosing one object out of two objects remains at 50%.

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