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Probability and Recurrence Relation

Suppose a coin is flipped and a die is rolled. Let E1 denote the event "the coin shows a tail", let E2 denote the event "the dies shows a 3", and let E3 denote the event "the coin shows heads and the die shows an odd number". Are E1 and E2 mutually exclusive?

A family of four children. Assume that it is equally probable for a boy or a girl to be born. What is the probability of exactly two girls?

Find a recurrence relation and initial conditions that generate a sequence that begins with the given term.

3,6,9,15,24,39,...

Solution Preview

Suppose a coin is flipped and a die is rolled. Let E1 denote the event "the coin shows a tail", let E2 denote the event "the dies shows a 3", and let E3 denote the event "the coin shows heads and the die shows an odd number". Are E1 and E2 mutually exclusive?

E1 and E2 are NOT mutually exclusive because both can happen at the same time. If they were mutually exclusive, then the coin showing tails would somehow prevent the die showing a three and vice versa. The ...

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