Question

amar can either take a course in computer or mathematics.If Amar takes the computer course then he will get an A grade with probability (1)/(2) if he takes the mathematics course then he will get an A grade with probability (1)/(3) Amar decides to base his decision on the flip of a fair coin.What is the probability that Amar will get an A grade in mathematics?​

Answer 1

Answer:

1 and -1 are the only rational numbers which are their own reciprocals. No other rational number is its own reciprocal. We know that there is no rational number which when multiplied with 0, gives 1.

Answer 2

Answer:

P(A) = 1/6

Explanation :

• Define the problem: Amar has to choose between taking a computer course or a mathematics course. The probability of getting an A grade in the computer course is 1/2 and the probability of getting an A grade in the mathematics course is 1/3. Amar will choose the course based on the flip of a fair coin. We need to find the probability that Amar will get an A grade in the mathematics course.

• Use probability rules: We can use the law of total probability to find the probability that Amar will get an A grade in the mathematics course. This law states that:

P(A) = P(A|B)P(B) + P(A|B')P(B')

where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, P(B') is the probability of event B not occurring, P(A|B) is the conditional probability of event A occurring given that event B has occurred, and P(A|B') is the conditional probability of event A occurring given that event B has not occurred.

• Apply the law of total probability: Let's define the events as follows:

A = Amar gets an A grade in the mathematics course

B = Amar chooses to take the mathematics course

B' = Amar chooses to take the computer course

We know that P(A|B) = 1/3 and P(A|B') = 0, and we also know that P(B) = P(B') = 1/2 because Amar is equally likely to choose either course. Therefore:

P(A) = (1/3)(1/2) + (0)(1/2)

P(A) = 1/6

• Interpret the result: The probability that Amar will get an A grade in the mathematics course is 1/6, which is less than the probability of getting an A grade in the computer course. Therefore, if Amar wants to maximize his chances of getting an A grade, he should choose to take the computer course.