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Probability

Probability

IP 4

A fair die is rolled once. Let: \[E=\{\text{even number}\hspace{0.15em}\},\qquad G=\{\text{number greater than}\hspace{0.5em}4\}.\]

  1. Find \(P(E)\), \(P(G)\), and \(P(E\cap G)\).

  2. Determine whether \(E\) and \(G\) are independent.

  3. Determine whether they are mutually exclusive.

Solution:

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Answer:(a) \(P(E)=\frac12,\ P(G)=\frac13,\ P(E\cap G)=\frac16\). (b) Independent. (c) Not mutually exclusive.

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