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An experiment consists of asking 2 politicians if they are in favor of former president
Estrada‟s home arrest. Use “N” for no, “Y“ for yes and “U“ for undecided.
a.) Determine the number of elements and list the elements in the sample space S.
b.) List all the elements of the following events and find its probability.
F = event that only 1 politician is in favor
A = event that at least 1 politician is against
U = event that at most 1 politician is undecided.
thank you so much
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The solution by @PChill is partly correct and partly wrong.
Below I placed my solution and marked where I agree with @PChill and where I do not agree.
**a) Determine the number of elements and list the elements in the sample space S.**
* **Sample Space (S):**
* S = {(Y, Y), (Y, N), (Y, U), (N, Y), (N, N), (N, U), (U, Y), (U, N), (U, U)}
* where (Y, Y) represents the first politician saying "Yes" and the second saying "Yes," and so on.
* **Number of elements in S:** 9
**b) List all the elements of the following events and find its probability.**
* **F = event that only 1 politician is in favor:**
* F = {(Y, N), (N, Y)}, (Y,U), (U,Y)) <<<---=-== different from @PChill
* P(F) = 4/9 <<<---=-== different from @PChill
* **A = event that at least 1 politician is against:**
* A = {(Y, N), (N, Y), (N, N), (N, U), (U, N)) <<<---=-== different from @PChill
* P(A) = 5/9 <<<---=-== different from @PChill
* **U = event that at most 1 politician is undecided:**
* U = {(Y, Y), (Y, N), (N, Y), (N, N), (Y, U), (U, Y)} <<<---=-== agree with @PChill
* P(U) = 6/9 = 2/3 <<<---=-== agree with @PChill
Solved.
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**Note:**
* We are assuming that each outcome in the sample space is equally likely.
* The probabilities are calculated by dividing the number of outcomes in the event by the total number of possible outcomes in the sample space.