s":[{"id":"f1c2f409-b127-48c4-9cee-2e62a363b23f","cardType":"cloze","front":"

The event that both $A$ and $B$ occur is their [ ].

","back":"

The event that both $A$ and $B$ occur is their intersection, $A\\cap B$.

","points":null,"mcqOptions":null},{"id":"fecafc74-bf77-42d5-a4c0-713517c9db3f","cardType":"cloze","front":"

The event that $A$, $B$, or both occur is their [ ].

","back":"

The event that $A$, $B$, or both occur is their union, $A\\cup B$.

","points":null,"mcqOptions":null},{"id":"8098dfb5-ee19-4989-9e17-eae5616c8360","cardType":"cloze","front":"

The general addition rule is $\\text{[...]}$.

","back":"

The general addition rule is $\\boxed{P(A\\cup B)=P(A)+P(B)-P(A\\cap B)}$.

","points":null,"mcqOptions":null},{"id":"ea134b47-899f-4b40-aeb0-97f7c62f487b","cardType":"basic","front":"Why is $P(A\\cap B)$ subtracted in the general addition rule?","back":"

The intersection was counted twice when $P(A)$ and $P(B)$ were added.

","points":2,"mcqOptions":null},{"id":"50e03053-ccc7-45f5-9c3d-eb1fc07b7b19","cardType":"cloze","front":"

Mutually exclusive events satisfy $\\text{[...]}$.

","back":"

Mutually exclusive events satisfy $\\boxed{P(A\\cap B)=0}$.

","points":null,"mcqOptions":null},{"id":"792d302c-f1c5-4e5c-83d2-222e72bffa17","cardType":"basic","front":"How does the addition rule simplify when $A$ and $B$ are mutually exclusive?","back":"

$P(A\\cup B)=P(A)+P(B)$

","points":1,"mcqOptions":null},{"id":"8d56a0f5-1eae-4354-9108-87d47c0776a4","cardType":"basic","front":"A component is repairable with probability $0.07$ or rejected with probability $0.02$. These classifications are mutually exclusive. Find $P(\\text{not standard})$.","back":"

$0.07+0.02=0.09$

","points":1,"mcqOptions":null},{"id":"57ec1f47-f2fe-44b3-a5f7-d416695ba89a","cardType":"basic","front":"Given $P(A)=0.55$, $P(B)=0.40$ and $P(A\\cap B)=0.18$, find $P(A\\cup B)$.","back":"

$0.55+0.40-0.18=0.77$

","points":1,"mcqOptions":null},{"id":"46c5e69e-b959-4640-adca-a3a27ce50bd1","cardType":"cloze","front":"

Events $A$ and $B$ are independent when $\\text{[...]}$.

","back":"

Events $A$ and $B$ are independent when $\\boxed{P(A\\cap B)=P(A)P(B)}$.

","points":null,"mcqOptions":null},{"id":"fea70842-8d1c-4ef3-951d-292365447c8f","cardType":"cloze","front":"

If $A$ and $B$ are independent, then $\\text{[...]}$.

","back":"

If $A$ and $B$ are independent, then $\\boxed{P(A\\mid B)=P(A)}$.

","points":null,"mcqOptions":null},{"id":"bac5ee0e-e2e4-4913-b20f-8cce2bc2ed9c","cardType":"basic","front":"When is multiplying $P(A)$ and $P(B)$ justified to find $P(A\\cap B)$?","back":"

When $A$ and $B$ are independent.

","points":1,"mcqOptions":null},{"id":"71ecfd22-7ab4-44ae-9f8a-9ce386f11d8a","cardType":"basic","front":"A biased coin has $P(H)=0.6$. Independent tosses produce HHT. Find $P(\\text{HHT})$.","back":"

$0.6\\times0.6\\times0.4=0.144$

","points":1,"mcqOptions":null},{"id":"85decec7-17a9-4bdc-8380-e5db40cbaf58","cardType":"basic","front":"A biased coin with $P(H)=0.6$ is tossed independently three times. Find the probability of exactly two heads.","back":"

$3\\times(0.6)^2\\times0.4=0.432$

","points":2,"mcqOptions":null},{"id":"f06fa08c-2865-4225-b50c-193a614b3211","cardType":"basic","front":"Why can the probabilities of HHT, HTH and THH be added?","back":"

The three sequences are mutually exclusive.

","points":2,"mcqOptions":null},{"id":"981cbb6e-be7f-4e74-9122-fb4b53242cf5","cardType":"basic","front":"Given $P(A)=0.

2.3.5 Mutually exclusive and independent events Flashcards

2.3.5 Mutually exclusive and independent events Flashcards