Questions: Let the sample space be S=1,2,3,4,5,6,7,8,9,10. Suppose the outcomes are equally likely. Compute the probability of the event E=1,3,5,6. P(E)= (Type an integer or a decimal. Do not round.)

Let the sample space be S=1,2,3,4,5,6,7,8,9,10. Suppose the outcomes are equally likely. Compute the probability of the event E=1,3,5,6. P(E)= (Type an integer or a decimal. Do not round.)
Transcript text: Let the sample space be $S=\{1,2,3,4,5,6,7,8,9,10\}$. Suppose the outcomes are equally likely. Compute the probability of the event $E=\{1,3,5,6\}$. $P(E)=$ $\square$ (Type an integer or a decimal. Do not round.)
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Solution

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Solution Steps

To find the probability of event \( E \) occurring, we need to divide the number of favorable outcomes (elements in \( E \)) by the total number of possible outcomes (elements in \( S \)).

Solution Approach
  1. Count the number of elements in the sample space \( S \).
  2. Count the number of elements in the event \( E \).
  3. Divide the number of elements in \( E \) by the number of elements in \( S \).
Step 1: Define the Sample Space and Event

Let the sample space be \( S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \) and the event be \( E = \{1, 3, 5, 6\} \).

Step 2: Count the Number of Elements

The number of elements in the sample space \( S \) is \( |S| = 10 \). The number of elements in the event \( E \) is \( |E| = 4 \).

Step 3: Calculate the Probability

The probability of the event \( E \) occurring is given by: \[ P(E) = \frac{|E|}{|S|} = \frac{4}{10} = 0.4 \]

Final Answer

\[ \boxed{0.4} \]

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