d944269-070c-4675-af01-0fc76a7a63fe","cardType":"basic","front":"What does the notation $P(B \\mid A)$ represent?","back":"The conditional probability of B occurring given that A has already occurred.","points":1},{"id":"b16ac9f5-26c7-489b-9de2-1c2aec833e7c","cardType":"basic","front":"How do you calculate the probability of a specific sequence of events (a single route) in a tree diagram?","back":"Multiply the probabilities along the branches.","points":1},{"id":"e72d5737-7652-4b90-84a2-6dd1fb00472d","cardType":"cloze","front":"The rule for finding the probability of a sequence of events is $$P(A \\text{ and } B) = \\text{[...]}$$.","back":"The rule for finding the probability of a sequence of events is $$P(A \\text{ and } B) = \\boxed{P(A) \\times P(B \\mid A)}$$.","points":null},{"id":"e225c290-8305-45db-a9b2-78d379161d1a","cardType":"basic","front":"In a \"without replacement\" scenario, what two things change for the second choice?","back":"

The total number of items (denominator) decreases by 1.
The number of items of the chosen category (numerator) decreases by 1.

","points":2},{"id":"3c647250-ea21-4555-8c47-046ced9f0c52","cardType":"basic","front":"When should you add separate routes together in a probability problem?","back":"When the routes are mutually exclusive outcomes (e.g. \"Red-Red\" OR \"Green-Green\").","points":1},{"id":"560f80f7-e3ed-4a6b-8fab-3290874071b8","cardType":"basic","front":"How do you calculate the probability of picking \"one of each color\" from a bag of red and blue counters?","back":"Calculate the probability of Red-Blue and Blue-Red separately, then add them together.","points":2},{"id":"25d560c6-da4a-4991-bd3a-9ba95b166abf","cardType":"cloze","front":"If the probability of picking a blue pen on Monday is 0.65, the probability of picking a black pen is [ ].","back":"If the probability of picking a blue pen on Monday is 0.65, the probability of picking a black pen is $1 - 0.65 = 0.35$.","points":null},{"id":"dc66182e-cdbd-4c69-b0d2-7a35e8b1201a","cardType":"basic","front":"A bag has 5 red and 3 blue counters. If a red is picked first and not replaced, what is $P(\\text{red second} \\mid \\text{red first})$?","back":"$$\\frac{4}{7}$","points":2},{"id":"aab15fb2-5d51-449d-9f53-de32ba645c79","cardType":"cloze","front":"When picking two counters without replacement from a bag of 12, the denominator for the second branch will be [ ].","back":"When picking two counters without replacement from a bag of 12, the denominator for the second branch will be 11.","points":null},{"id":"18ca290a-dcb9-4351-8d95-8815964203fa","cardType":"basic","front":"What does it mean for two routes to be \"mutually exclusive\"?","back":"They cannot both happen at the same time.","points":1},{"id":"88565d54-8b2a-4c09-8a87-e32394a47b1d","cardType":"basic","front":"A bag has 7 red and 5 green counters. How do you set up the calculation for \"both counters are the same color\" (without replacement)?","back":"$$(\\frac{7}{12} \\times \\frac{6}{11}) + (\\frac{5}{12} \\times \\frac{4}{11})$","points":2},{"id":"79ebaa0b-3b9a-43ff-9a28-2187819c34bf","cardType":"basic","front":"Why is the calculation for \"different colors\" usually more complex than for a specific sequence like \"Black then Red\"?","back":"It usually involves two different orders (BR and RB) that must be added.","points":2},{"id":"e272e311-2a2e-48d1-90d7-7dd2360495ce","cardType":"cloze","front":"In a Venn diagram, the region representing \"Tea and Coffee but not Juice\" excludes the [ ] where all three meet.","back":"In a Venn diagram, the regi

Conditional Probability Flashcards

Conditional Probability Flashcards

Conditional Probability Flashcards

Conditional Probability Flashcards