Conditional probability: Difference between revisions

Revision as of 19:55, 14 November 2022

Revision as of 09:09, 17 November 2022

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<math>P(dot \ received) = \frac{9}{10}\times\frac{3}{7} + \frac{1}{10}\times\frac{4}{7} = \frac{31}{70}</math>

Now, <math>P(dot \ sent \mid dot \ received)</math> can be calculated:

<math>P(dot \ sent \mid dot \ received) = P(dot \ received \mid dot \ sent) \frac{P(dot \ sent)}{P(dot \ received)} = \frac{9}{10}\times \frac{\frac{3}{7}}{\frac{31}{70}} = \frac{27}{31}</math><ref>{{Cite web|title=Conditional Probability and Independence|url=http://www.math.ntu.edu.tw/~hchen/teaching/StatInference/notes/lecture4.pdf|access-date=2021-12-22}}</ref>