# Mathematics 1228A/B Lecture Notes - Lecture 2: Equiprobability, Sample Space, Dionne Quintuplets

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Published on 2 Aug 2020

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2.3 Equiprobable Sample Spaces!

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Deﬁne: !

A sample space is called equiprobable if every sample point is eqully likely to occur!

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Theorem:!

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"If S is an equiprobable space, then for any sample point a, Pr[a]=1/n(s), so for any event E,!

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Example 2.6!

A fair die is rolled. What is the probability that a number other than 6 comes up?!

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Example 2.7" !

A single card is turned up from a well-shuﬄed deck. What is the probability that the cardis a black face card.!

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Example 2.8!

Two fair dice are rolled. !

What is the probability that the sum is 9.!

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Example 2.9!

Recall the Bobbsey family, which has 2 set of twins, and the Dionne family, which has 5 quintuplulets!

They all arranged at random!

What is the probability that bobbsey is beside his/her twin and the dionnes are all grouped together.!

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Pr Enn equally probably occur

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Sall pairs Li jwith eachof iJbeing from I6inclusive

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## Document Summary

A sample space is called equiprobable if every sample point is eqully likely to occur. If s is an equiprobable space, then for any sample point a, pr[a]=1/n(s), so for any event e, 5 i 2 3. 4 5 63 each is equallylikely so s is equiprobable n s 6. I 2 3,4 5 w n e 5. A single card is turned up from a well-shu ed deck. What is the probability that the cardis a black face card. What is the probability that the sum is 9. S all pairs li j with eachof i o. It is a samplespacefewtosstwodice butnot equiprobable not all. Recall the bobbsey family, which has 2 set of twins, and the dionne family, which has 5 quintuplulets. What is the probability that bobbsey is beside his/her twin and the dionnes are all grouped together. come up with the same probability u not equally likely. The dionne quintuplets are going on a airplane trip.