eac-4718-a343-209e77d828c7","topicSlug":"probability-2","cards":[{"id":"113aa6e6-69d1-40f5-a22b-ffb273281bde","cardType":"basic","front":"What does $A\\cap B$ mean?","back":"Events $A$ and $B$ both occur.","points":1,"mcqOptions":null},{"id":"ce67c3c1-416a-4e76-a101-8671f487d82b","cardType":"basic","front":"What does $A\\cup B$ mean?","back":"$A$ or $B$, or both, occurs.","points":1,"mcqOptions":null},{"id":"959e94a2-d1f8-4faf-b411-2d81c5265c57","cardType":"basic","front":"What event is represented by $A'$?","back":"The event that $A$ does not occur.","points":1,"mcqOptions":null},{"id":"48f1f8bb-7ed5-41fe-8746-335b025f5221","cardType":"cloze","front":"Every probability satisfies $\\text{[...]}$.","back":"Every probability satisfies $\\boxed{0\\le P(A)\\le 1}$.","points":null,"mcqOptions":null},{"id":"67816c0f-b261-4a46-8dfd-b4f9ce237bcd","cardType":"basic","front":"If $P(A)=0.37$, find $P(A')$.","back":"$0.63$","points":1,"mcqOptions":null},{"id":"4b0f0149-193f-4be1-87a9-8b2ba5de3404","cardType":"cloze","front":"The complement rule is $\\text{[...]}$.","back":"The complement rule is $\\boxed{P(A')=1-P(A)}$.","points":null,"mcqOptions":null},{"id":"ab6ab937-7261-4c17-a785-bbd938a761df","cardType":"basic","front":"What value identifies impossible and certain events?","back":"

Impossible: $P(A)=0$
Certain: $P(A)=1$

","points":2,"mcqOptions":null},{"id":"e3b977de-df45-413a-92e2-7383383eff11","cardType":"basic","front":"What question tests whether two events are mutually exclusive?","back":"Can both events happen in the same trial?","points":1,"mcqOptions":null},{"id":"5a06af5f-fa77-48a6-8a42-4fd098f26163","cardType":"basic","front":"What intersection probability must mutually exclusive events have?","back":"$P(A\\cap B)=0$","points":1,"mcqOptions":null},{"id":"079f725c-bbc8-4b38-bfc3-31ec20a36af9","cardType":"cloze","front":"For mutually exclusive events, $\\text{[...]}$.","back":"For mutually exclusive events, $\\boxed{P(A\\cup B)=P(A)+P(B)}$.","points":null,"mcqOptions":null},{"id":"1bb9d061-5c4a-41e2-8440-f203d9ad10a1","cardType":"basic","front":"Why is $P(A\\cap B)$ subtracted in the general addition law?","back":"The intersection was counted twice.","points":2,"mcqOptions":null},{"id":"e6945fc5-5f58-4df4-bf40-1d1d41c19607","cardType":"cloze","front":"The general addition law is $\\text{[...]}$.","back":"The general addition law is $\\boxed{P(A\\cup B)=P(A)+P(B)-P(A\\cap B)}$.","points":null,"mcqOptions":null},{"id":"6b3a5371-ce1b-497b-8b86-147c1bba0f44","cardType":"basic","front":"Given $P(A)=0.4$, $P(B)=0.35$ and $P(A\\cap B)=0.12$, find $P(A\\cup B)$.","back":"$0.63$","points":2,"mcqOptions":null},{"id":"22491c33-7278-4ebb-b4ca-128345c0c66c","cardType":"basic","front":"What effect does event $A$ have on event $B$ when they are independent?","back":"$$A$ occurring does not change $P(B)$.","points":1,"mcqOptions":null},{"id":"b317fd27-b20b-4487-94f9-13e10847345e","cardType":"cloze","front":"For independent events, $\\text{[...]}$.","back":"For independent events, $\\boxed{P(A\\cap B)=P(A)P(B)}$.","points":null,"mcqOptions":null},{"id":"833e31f9-519f-4b31-a7c5-d70fd35db4aa","cardType":"basic","front":"How can given probabilities be used to test whether $A$ and $B$ are independent?","back":"Check whether $P(A\\cap B)=P(A)P(B)$.","points":2,"mcqOptions":null},{"id":"61fb4c10-d585-48ae-b259-b73cff4820a8","cardType":"basic","front":"Given $P(A)=0.4$, $P(B)=0.5$ and $P(A\\cap B)=0.18$, are $A$ and $B$ independent?","back":"No, because $0.18\\ne0.4(0.5)=0.20$.","points":2,"mcqOptions":null},{"id":"32e7a221-5bde-40fc-a6ed-bf8117f10690","cardType":"basic","front":"A coin has $P(H)=0.6$ and is tossed independently three times. Find $P(HTH)$.","back":"$0.6\\times0.4\\times0.6=0.144$","points":2,"mcqOptions":null},{"id":"7b989d90-c9a5-4698-a4cb-bfb1e3487804","cardType":"bas

2.3.1 Probability Flashcards

2.3.1 Probability Flashcards