Problem

From the sample space $S=\{1,2,3,4, \ldots, 15\}$ a single number is to be selected at random. Given the following events, find the indicated probability. A: The selected number is even. $B$ : The selected number is a multiple of 4. . $C$ : The selected number is a prime number. $P(A \mid B)$ $P(A \mid B)=\square$ (Simplify your answer. Type an integer or a fraction.)

Solution

Step 1 :From the sample space $S=\{1,2,3,4, \ldots, 15\}$ a single number is to be selected at random. Given the following events, find the indicated probability.

Step 2 :A: The selected number is even.

Step 3 :$B$ : The selected number is a multiple of 4.

Step 4 :$C$ : The selected number is a prime number.

Step 5 :We are asked to find $P(A \mid B)$, the conditional probability of event A (the selected number is even) given that event B (the selected number is a multiple of 4) has occurred.

Step 6 :In other words, we want to find the probability that the selected number is even, given that we know it is a multiple of 4.

Step 7 :Since all multiples of 4 are even, if we know that the selected number is a multiple of 4, we can be certain that it is also even. Therefore, the probability of event A given event B is 1.

Step 8 :Final Answer: $P(A \mid B)=\boxed{1}$

From Solvely APP
Source: https://solvelyapp.com/problems/8682/

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