The value of the P(F) and P(E ∩ F) and P(F | E) and P(E) according to the permutation is 5/36, 1/36, 1/6,1/6.
According to the statement
we have given that the E denote the event that the number falling uppermost on the first die is 2, and let F denote the event that the sum of the numbers falling uppermost is 8
And we have to solve the given statements according to this.
So,
According to the statement,
P(E) = 1/6
For event F, the Sample space is:
F = (2,6), (3,5), (4,4) (6,2), (5,3)
Here First no. of each pair denotes first dice and second one denoted the second dice.
So,
A.
P(F) = 1/6 * 1/6 + 1/6 * 1/6 + 1/6 * 1/6 + 1/6 * 1/6 + 1/6 * 1/6
P(F) = 5/36.
B.
P(E ∩ F) = 1/6 *1/6
P(E ∩ F) = 1/36.
C.
P(F | E) = (1/36) / (1/6)
P(F | E) = 1/6.
D.
P(E) = 1/6.
So, The value of the P(F) and P(E ∩ F) and P(F | E) and P(E) according to the permutation is 5/36, 1/36, 1/6,1/6.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
A pair of fair dice is rolled. Let E denote the event that the number falling uppermost on the first die is 2, and let F denote the event that the sum of the numbers falling uppermost is 8. (Round your answers to three decimal places.)
(a) Compute P(F).
(b) Compute P(E ∩ F).
(c) Compute P(F | E).
(d) Compute P(E).
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