Question

quiz 6.4.1 - adding probabilities
this quiz will test your knowledge on when and how to add probabilities together.
value: 3
jamal rolls a fair number cube (a cube with six sides, each containing a different number from 1 - 6). what is the probability that he has rolled a 5 given that he has rolled an even number?
○ a. 1
○ b. 0
○ c. 1/8
○ d. 1/3

1/8

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Explanation:

Step1: Identify favorable and total cases

The even - numbered outcomes on a number cube are 2, 4, 6. The number 5 is not an even number. So, the number of favorable outcomes (rolling a 5 given an even number is rolled) is 0, and the number of total even - numbered outcomes is 3.

Step2: Calculate the probability

The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, event \(A\) is rolling a 5 and event \(B\) is rolling an even number. Since \(A\cap B = \varnothing\) (the empty set, as 5 is not even), \(n(A\cap B)=0\) and \(n(B) = 3\). So, \(P(A|B)=\frac{0}{3}=0\).

Answer:

B. 0