A student is taking a multiple choice test where each question have 5 possible answers of which only one is right. If the student knows the answer the student answers correctly, otherwise there is a 20% probability of correct answer. Assume the student knows 70% of the questions.
a. What is the probability of the student answering a question correct?
To calculate the probability of the student answering a question correctly, we need to consider two scenarios:
1. When the student knows the answer:
Since the student knows 70% of the questions, the probability of answering a question correctly when the student knows the answer is 100%.
2. When the student doesn't know the answer:
In this case, there is a 20% probability of randomly selecting the correct answer out of the 5 possible choices.
Thus, the overall probability of the student answering a question correctly can be calculated by multiplying the probability of each scenario with its respective weight (probability of knowing the answer and probability of not knowing the answer):
Probability of answering correctly = (Probability of knowing the answer * 100%) + (Probability of not knowing the answer * 20%)
Probability of knowing the answer = 70% = 0.7
Probability of not knowing the answer = 30% = 0.3
Using these values, we can calculate the probability of the student answering a question correctly:
Probability of answering correctly = (0.7 * 100%) + (0.3 * 20%)
Probability of answering correctly = 70% + 6%
Probability of answering correctly = 76%
Therefore, the probability of the student answering a question correctly is 76%.
To find the probability of the student answering a question correctly, we need to consider two scenarios:
1. When the student knows the answer.
2. When the student does not know the answer.
Let's calculate the probability of each scenario and then combine them.
1. Probability when the student knows the answer:
Since the student knows 70% of the questions, the probability of getting the correct answer in this case is 100% (or 1).
2. Probability when the student does not know the answer:
In this case, the student has a 20% probability of randomly guessing the correct answer, as mentioned in the question.
Now, let's calculate the probability of the student not knowing the answer, which is the complement of knowing the answer:
Probability of not knowing the answer = 1 - Probability of knowing the answer
= 1 - 0.7
= 0.3
Now, let's calculate the overall probability of answering the question correctly by combining both scenarios:
Probability of answering correctly = (Probability of knowing the answer × Probability of answering correctly when knowing) + (Probability of not knowing the answer × Probability of answering correctly when not knowing)
= (0.7 × 1) + (0.3 × 0.2)
= 0.7 + 0.06
= 0.76
Therefore, the probability of the student answering a question correctly is 0.76 or 76%.