Final answer:
The probability of passing both exams is calculated using the principle of inclusion and exclusion, yielding a result that does not match the provided options. Without further information on the dependence between the exams, a definitive answer cannot be provided.
Step-by-step explanation:
The question pertains to the probability of a randomly chosen student passing both exams, given individual pass probabilities and the probability of passing at least one. To compute this, we use the principle of inclusion and exclusion for probabilities. The formula states:
P(A and B) = P(A) + P(B) - P(A or B)
Where:
- P(A and B) is the probability of passing both exams.
- P(A) is the probability of passing the first exam (0.8).
- P(B) is the probability of passing the second exam (0.7).
- P(A or B) is the probability of passing at least one exam (0.95).
Substituting the given values, we get:
P(A and B) = 0.8 + 0.7 - 0.95 = 0.55.
Since 0.55 is not one of the options provided, we realize there might be a misunderstanding. It's possible that the event's probabilities are not independent, and thus the provided probabilities imply some degree of overlap. For example, passing the first exam might improve the chance of passing the second. Without information about the dependence of the events, we're unable to select from the given options.