DSA Studio

Probability Checkpoint

Trace the representation, diagnose a boundary failure, and reconstruct a changed case.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. P(A)=0.5, P(B)=0.4, P(A and B)=0.2. What is P(A or B)? Select one.

Select one answer.

2. A class has prior probability 0.1. A flag occurs with probability 0.8 in that class and 0.2 outside it. Given a flag, what is the class probability? Select one.

Select one answer.

3. Two independent fair coin flips are observed. Given that at least one is heads, what is the chance both are heads? Select one.

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4. A discrete distribution assigns probabilities 0.15, 0.25, and p to its only three outcomes. What is p?
5. A and B are disjoint and both have positive probability. Are they independent? Select one.

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6. The API returns 0.0 for conditional_probability(0.0,0.0). What does that establish? Select one.

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7. Among 200 messages, 40 are spam; 30 spam and 20 ordinary messages are flagged. What is P(spam | flagged)? Answer as a decimal.
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