A number is randomly selected from the set {1,2, --. , 23!} (note that there is a factorial!). For k = 1,2,-, 20, define the events Ak = {the selected number is divisible by k}. Find the following probabilities. (a) P(A10),P(A15). (b) P(A10 A15 (c) P(A10 U A15).

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A number is randomly selected from the set {1,2, · , 23!} (note that there is a factorial!). For k = 1,2,· .. , 20,
define the events
Ak = {the selected number is divisible by k}.
Find the following probabilities.
( a) P(A10), P (Α15).
(b) P (A10|415).
|A15
(c) P(A10 U A15).
(d) P(A10 U A15 U A21).
(e) P(A10 U A15 A21 ).
(f) P (A10 A15, A21).
Transcribed Image Text:A number is randomly selected from the set {1,2, · , 23!} (note that there is a factorial!). For k = 1,2,· .. , 20, define the events Ak = {the selected number is divisible by k}. Find the following probabilities. ( a) P(A10), P (Α15). (b) P (A10|415). |A15 (c) P(A10 U A15). (d) P(A10 U A15 U A21). (e) P(A10 U A15 A21 ). (f) P (A10 A15, A21).
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Probability:

The probability of an event is the proportion of the number of times the event occurs to the total number of events that is the sample space. It gives the chance of a particular event to be the output for an experiment. (OR) It is the ratio of the number of events that occur to the sample space of the experiment. It is basically the chance of getting some particular events from the experiment.

Conditional Probability:

It the probability with certain conditions that are applied to the events and calculating its chance.

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