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Apply probability across unfamiliar problems: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Define the sample space before assigning probabilities. Decide whether selection replaces an item and whether the second event depends on the first.
A fair six-sided die is rolled. What is the probability of a result greater than 4? Enter a fraction.
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A box contains 5 red and 3 blue balls. Two are drawn without replacement. What is the probability both are blue? Enter a fraction.
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Independent events A and B have probabilities .4 and .3. What is the probability that at least one occurs?
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Of 80 people, 45 speak language A, 30 speak B and 12 speak both. How many speak neither?
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Among 100 people, 50 use A, 40 use B, 30 use C; pairwise overlaps AB, AC and BC are 20,15 and 10, each including the 5 who use all three. How many use at least one?
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A medical-study table has 24 participants with both condition A and exposure B, and 60 participants with exposure B overall. What fraction of exposed participants have A?
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Events A and B are mutually exclusive, with probabilities .2 and .5. What is P(A or B)?
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For events A and B, P(A)=.7, P(B)=.6 and P(A and B)=.4. What is P(neither)?
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A bag holds cards numbered 1 through 12. Given that a uniformly drawn card is even, what is the probability it is divisible by 3? Enter a fraction.
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A game pays 10 with probability .2 and 0 otherwise. Its entry fee is 3. What is the expected net payoff?
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A device works with probability .9. Two devices work independently. What is the probability exactly one works?
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Factory A makes 60 percent of a shipment with a 2 percent defect rate; factory B makes the rest with a 5 percent defect rate. Given that a randomly chosen item is defective, what is the probability it came from B? Enter a fraction.
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Check with a complement or an explicit count of outcomes, ensuring that overlapping events are not added twice.