Question

In: Statistics and Probability

During a study group, you and your friend discover that you have arrived (independently) at different...

During a study group, you and your friend discover that you have arrived (independently) at different solutions to a math problem. From past experience, you know that you generally answer questions correctly 75% of the time, but your friend answers questions correctly 90% of the time.

a) In general, how often does it happen that you answer a question correctly and your friend answers incorrectly?

b) In general, how often does it happen that you answer a question incorrectly and your friend answers correctly?

c) In general, how often does it happen that one of the two of you answers a question correctly and the other answers incorrectly?

d) The TA confirms that one of your two answers is correct, but refuses to say whose. What is the probability that yours is the correct answer?

Expert Solution

Let CM denote the event of me answering the question correctly and Let CF denote the event of my friend answering the question correctly.
We are given the following information:

a) Probability of me answering correctly and friend answering incorrectly:

probability of me answering it right * probability of friend answering it incorrectly

b)Probability of me answering a question incorrectly and your friend answers correctly:

probability of friend answering it right * probability of me answering it incorrectly

c)Probability one of the two of you answers a question correctly :

probability of friend answering it right * probability of me answering it incorrectly OR probability of me answering it right * probability of friend answering it incorrectly

d) We need to calculate the probability :

orchestra answered 1 year ago

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