(15 points) Refer to the sample spaces shown in the figures below. The sample sp
ID: 3057370 • Letter: #
Question
(15 points) Refer to the sample spaces shown in the figures below. The sample space has six basic outcomes, and the probability for each outcome is shown. Two events are defined on each sample space. 4. In the sample space on the left, event E contains four basic outcomes and event F contains three basic outcomes. Note two outcomes are common for the two events. In the sample space on the right, event B contains five basic outcomes and event B* contains one basic outcome. x1 X2X3 (3 points) What is P(E) (3 points) What is the P(F) (3 points) What is the probability of the intersection of the two events E and F. That is P(ENF) (3 points) What is the probability of the union P(E U F) (2 points) Using the sample space on the left, show an equivalent method to prove that the probability of a union can be found by equation 2-5 from the text (1 points) For the sample space on the right, what is the probability P(B)?Explanation / Answer
Solution:
1. P (E) = a + b + c + d = 4/6
2. P (F) = b + c + e = 3/6
3. P (E F) = b + e = 2/6
4. P (E U F) = a + b + 2c + d = 5/6
5. P (E U F) = P (E) + P (F) - P (E F)
P (E U F) = a + b + c + d + b + c + e - b - e
P (E U F) = a + b + 2c + d
P (E U F) = 5/6
6. P (B) = X1 + X2 + X3 + X4 + X5 = 4/6
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