Question

chapter 4.3 homework
score: 4/42 answered: 4/33
question 5
4.3 conditional probability. calculating conditional probabilities.
suppose you roll 2 dice. what is the probability that the sum of the 2 dice is exactly 5, given that the 1st dice is a 2?
express your answer as a reduced fraction.
question help: video message instructor

Explanation:

Step1: Determine the condition

The first - die shows 2. When the first die shows 2, the possible outcomes for the two - dice roll are of the form (2, x), where x can take values from 1 to 6. So there are 6 possible outcomes.

Step2: Find the favorable outcomes

We want the sum of the two dice to be 5 and the first die to be 2. Let the first die be \(a = 2\) and the second die be \(b\). We know that \(a + b=5\), so if \(a = 2\), then \(b = 3\). There is 1 favorable outcome, which is (2, 3).

Step3: Calculate the conditional probability

The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, \(n(B) = 6\) (number of outcomes when the first die is 2) and \(n(A\cap B)=1\) (the outcome where the first die is 2 and the sum is 5). So the probability is \(\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)