SOLUTION: If we roll a die two times, determine whether the following pairs of events are independent or dependent. Event A is rolling a 3 on the first die. Event B is getting a sum of mor

Question 1168570: If we roll a die two times, determine whether the following pairs of events are independent or dependent.
Event A is rolling a 3 on the first die. Event B is getting a sum of more than 6 with the two dice?
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Let's determine if events A and B are independent or dependent.
**1. Define the Events**
* **Event A:** Rolling a 3 on the first die.
* **Event B:** Getting a sum of more than 6 with the two dice.
**2. Calculate Probabilities**
* **P(A):** The probability of rolling a 3 on the first die is 1/6 (since there's one favorable outcome out of six).
* **P(B):** To find P(B), we need to count the pairs of dice rolls that sum to more than 6.
* Possible pairs: (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
* There are 21 pairs that sum to more than 6.
* Total possible pairs: 6 * 6 = 36.
* P(B) = 21/36 = 7/12.
* **P(A and B):** The probability of both events A and B occurring.
* We need to count the pairs where the first die is a 3 and the sum is greater than 6.
* These pairs are: (3,4), (3,5), (3,6).
* P(A and B) = 3/36 = 1/12.
**3. Check for Independence**
* Two events are independent if P(A and B) = P(A) * P(B).
* Let's check:
* P(A) * P(B) = (1/6) * (7/12) = 7/72
* P(A and B) = 1/12 = 6/72
* Since 7/72 ≠ 6/72, P(A and B) ≠ P(A) * P(B).
**4. Conclusion**
* Therefore, events A and B are **dependent**.

RELATED QUESTIONS
If we roll a die two times, determine whether the following pairs of events are... (answered by ikleyn)

If we roll a die two times, determine whether the following pairs of events are... (answered by solver91311,Boreal)

If we roll a pair of dice, which of the following pairs of events are mutually exclusive? (answered by ikleyn)

Suppose a standard die is rolled twice. Let A be the event a 3 occurs on the first roll,... (answered by ewatrrr)

If we roll a pair of dice, which of the following pairs of events are mutually exclusive? (answered by ikleyn)

Please help me solve this Problem A balanced die is rolled twice. Consider the following (answered by stanbon)

A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll... (answered by oscargut)

You roll two six-sided fair dice. a. Let A be the event that the first die is odd and (answered by math_tutor2020)

if you roll a die 60 times what is the probability you would roll a 1 or 6?... (answered by edjones)