A student has a 70% chance of passing an exam. If he takes the exam twice, what

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Question: A student has a 70% chance of passing an exam. If he takes the exam twice, what is the probability that he passes at least once?

Options:

Correct Answer: 0.91

Solution:

The probability of passing at least once is 1 - (0.3^2) = 1 - 0.09 = 0.91.

A student has a 70% chance of passing an exam. If he takes the exam twice, what is the probability that he passes at least once?

A student has a 70% chance of passing an exam. If he takes the exam twice, what is the probability that he passes at least once?

Step 1: Understand that the student has a 70% chance of passing the exam. This means there is a 30% chance of failing the exam.
Step 2: Since the student takes the exam twice, we need to find the probability of failing both times.
Step 3: Calculate the probability of failing once, which is 0.3 (30%).
Step 4: To find the probability of failing both times, multiply the probability of failing once by itself: 0.3 * 0.3 = 0.09.
Step 5: Now, to find the probability of passing at least once, subtract the probability of failing both times from 1: 1 - 0.09 = 0.91.
Step 6: Therefore, the probability that the student passes at least once is 0.91 or 91%.

Probability of Independent Events – This concept involves calculating the probability of at least one success in multiple independent trials.
Complement Rule – This rule states that the probability of at least one success can be found by subtracting the probability of no successes from 1.