In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neither (events cannot be both disjoint and independent). a) You and a randomly selected student from your class both earn A's in this course. Independent Mutually Exclusive Neither b) You and your class partner both earn A's in this course. Independent Mutually Exclusive Neither c) If two events can occur at the same time, they must be independent. True False
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Since both events can occur at the same time (you can earn an A and the randomly selected student can also earn an A), the events are independent. ** Show more…
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In parts (a) and (b), identify whether the events are Mutually Exclusive, Independent, or Neither (events cannot be both disjoint and independent). a) You and a randomly selected student from your class both earn A's in this course. Independent Neither Mutually Exclusive b) You and your class partner both earn A's in this course. Neither Independent Mutually Exclusive c) If two events can occur at the same time, they must be independent. True False
Benjamin D.
In parts (a) and (b), identify whether the events are mutually exclusive, independent, or neither (events cannot be both mutually exclusive and independent). a) You and a randomly selected student from your class both earn B's in this course. mutually exclusive independent neither b) You and your class partner both earn B's in this course. neither mutually exclusive independent c) If two events can occur at the same time, they must be independent. true false
For two events $\mathrm{A}$ and $\mathrm{B}$, if $\mathrm{P}(\mathrm{a})=\mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{1}{4}$ and $\mathrm{P}(\mathrm{B} / \mathrm{A})=\frac{1}{2}$ then (a) $\mathrm{A}$ and $\mathrm{B}$ are independent (b) A and B are mutually exclusive (c) $\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)=\frac{3}{4}$ (d) $\mathrm{P}\left(\mathrm{B}^{\prime} \mid \mathrm{A}^{\prime}\right)=\frac{1}{2}$
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