Question

chapter 4.3 homework
score: 1/42 answered: 1/33
question 2
4.3 conditional probability. calculating conditional probabilities.
suppose you roll 2 dice. what is the pobability that the sum of the 2 dice is ≤ 10, given that the 1st dice is a 6?
express your answer as a fraction.
enter a fraction or integer (no mixed numbers)

Explanation:

Step1: Determine total outcomes when first die is 6

When the first die shows 6, the second die can take values from 1 - 6. So there are 6 total possible outcomes: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

Step2: Determine favorable outcomes

We want the sum of the two - dice to be ≤ 10. When the first die is 6, the pairs that satisfy this are (6,1), (6,2), (6,3), (6,4). So there are 4 favorable outcomes.

Step3: Calculate probability

The probability formula for conditional probability in this case is $P(A|B)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the probability that the sum of the two dice is ≤ 10 given that the first die is 6 is $\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$