There are 3 short questions on math test. for each question, 1 mark will be awarded for a correct answer and no mark for wrong answer. if the probability that mary correctly answers a question in a test is 2/3, determine the probability that mary correctly answers a question test is 2/3, determine the probability the probability that nary gets 2 marks in the test.
4/27
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
2/3 * 2/3 * 1/3 = ?
Well, Mary has a probability of 2/3 of answering a question correctly. So, the probability of her answering a question incorrectly would be 1 - 2/3 = 1/3.
To find the probability of Mary getting 2 marks on the test, we need to consider the different ways this can happen:
1. First question correct, second question correct, third question incorrect.
Probability: (2/3) * (2/3) * (1/3)
2. First question correct, second question incorrect, third question correct.
Probability: (2/3) * (1/3) * (2/3)
3. First question incorrect, second question correct, third question correct.
Probability: (1/3) * (2/3) * (2/3)
Now we add up the probabilities of these three scenarios to get the total probability of Mary getting 2 marks:
(2/3) * (2/3) * (1/3) + (2/3) * (1/3) * (2/3) + (1/3) * (2/3) * (2/3) = 12/81
Therefore, the probability that Mary gets 2 marks in the test is 12/81 or approximately 0.148.
To determine the probability that Mary gets 2 marks in the test, we need to consider the different possible scenarios.
Scenario 1: Mary answers 2 questions correctly and 1 question incorrectly.
The probability of Mary correctly answering a question is 2/3, and the probability of answering a question incorrectly is 1/3. Since there are 3 questions in total, the probability of this scenario is:
(2/3) * (2/3) * (1/3) = 4/27
Scenario 2: Mary answers all 3 questions correctly.
The probability of Mary correctly answering a question is 2/3. Since there are 3 questions in total, the probability of this scenario is:
(2/3) * (2/3) * (2/3) = 8/27
Scenario 3: Mary answers 1 question correctly and 2 questions incorrectly.
The probability of Mary correctly answering a question is 2/3, and the probability of answering a question incorrectly is 1/3. Since there are 3 questions in total, the probability of this scenario is:
(2/3) * (1/3) * (1/3) = 2/27
To find the probability that Mary gets 2 marks in the test, we need to add up the probabilities of scenarios 1 and 3:
4/27 + 2/27 = 6/27 = 2/9
Therefore, the probability that Mary gets 2 marks in the test is 2/9.
To determine the probability that Mary gets 2 marks in the test, we need to consider all possible combinations of correct and incorrect answers for the three questions.
Let's analyze the possible scenarios:
1. Mary answers all three questions correctly: The probability of this happening is (2/3)*(2/3)*(2/3) since each question has a 2/3 probability of being answered correctly. So, the probability for this scenario is (2/3)^3.
2. Mary answers two questions correctly and one question incorrectly: There are three ways this scenario can occur: CCI (correct, correct, incorrect), CIC (correct, incorrect, correct), or ICC (incorrect, correct, correct). The probability for each of these scenarios is (2/3)*(2/3)*(1/3) since one out of the three questions is answered incorrectly. Therefore, the overall probability for this scenario is 3 * (2/3)*(2/3)*(1/3).
3. Mary answers one question correctly and two questions incorrectly: Similar to the previous case, there are three ways this can occur: CII (correct, incorrect, incorrect), ICI (incorrect, correct, incorrect), or IIC (incorrect, incorrect, correct). The probability for each of these scenarios is (2/3)*(1/3)*(1/3) since only one out of the three questions is answered correctly. So, the overall probability for this scenario is 3 * (2/3)*(1/3)*(1/3).
4. Mary answers all three questions incorrectly: The probability of this happening is (1/3)*(1/3)*(1/3) since each question has a 1/3 probability of being answered incorrectly. So, the probability for this scenario is (1/3)^3.
To determine the probability that Mary gets 2 marks in the test, we need to add up the probabilities from scenarios 2 and 3 because those are the cases where she correctly answers two questions. Therefore, the final probability is:
Probability = (3 * (2/3)*(2/3)*(1/3)) + (3 * (2/3)*(1/3)*(1/3))
Simplifying,
Probability = (12/27) + (6/27)
Probability = 18/27
Simplifying further,
Probability = 2/3
Therefore, the probability that Mary gets 2 marks in the test is 2/3.