Question

chapter 4.3 homework
score: 3/42 answered: 3/33
question 4
4.3 conditional probability. calculating conditional probabilities.
suppose you roll 2 dice. what is the pobability that the sum of the 2 dice is ≤ 8, given that the 1st dice is a 5?
express your answer as a fraction.

Explanation:

Step1: Determine the sample - space given the condition

The first die shows a 5. When the first die is 5, the possible pairs of dice - rolls are (5,1), (5,2), (5,3), (5,4), (5,5), (5,6). So there are 6 possible outcomes.

Step2: Determine the favorable outcomes

We want the sum of the two dice to be ≤ 8. When the first die is 5, the pairs that satisfy this are (5,1), (5,2), (5,3). So there are 3 favorable outcomes.

Step3: Calculate the conditional probability

The formula for conditional probability is $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, the probability $P$ that the sum of the two dice is ≤ 8 given that the first die is 5 is the number of favorable outcomes divided by the number of possible outcomes. So $P=\frac{3}{6}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$