Question

1. zulerma has a pair of dice. she tossed the pair and wanted to know what the probability is of getting a sum of 6 or 9. what is the probability of getting a sum of 6 or 9?

options:
1/6
2/9
5/36
1/4
clear all

Explanation:

Step1: Find total outcomes

When tossing two dice, each die has 6 faces. So total outcomes = \(6\times6 = 36\).

Step2: Find outcomes for sum = 6

The pairs \((x,y)\) where \(x + y=6\) are: \((1,5),(2,4),(3,3),(4,2),(5,1)\). So 5 outcomes.

Step3: Find outcomes for sum = 9

The pairs \((x,y)\) where \(x + y = 9\) are: \((3,6),(4,5),(5,4),(6,3)\). So 4 outcomes.

Step4: Calculate favorable outcomes

Favorable outcomes (sum 6 or 9) = \(5 + 4=9\).

Step5: Calculate probability

Probability = \(\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{9}{36}=\frac{1}{4}\)? Wait, no, wait: Wait 5 + 4 is 9? Wait 5 (sum 6) + 4 (sum 9) = 9. Then 9/36 = 1/4? Wait no, wait 5 + 4 is 9? Wait 5 (sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)) → 5. Sum 9: (3,6),(4,5),(5,4),(6,3) → 4. So total favorable 5 + 4 = 9. Total outcomes 36. So 9/36 = 1/4? Wait but let's check again. Wait 5 + 4 is 9. 9/36 = 1/4. Wait but the options: 1/6, 2/9, 5/36, 1/4. Wait 9/36 = 1/4. So the answer is 1/4? Wait no, wait 5 + 4 is 9? Wait 5 (sum 6) and 4 (sum 9) → 9. 9/36 = 1/4. So the correct option is the one with 1/4. Wait but let's recalculate:

Wait sum of 6: possible pairs:

(1,5), (2,4), (3,3), (4,2), (5,1) → 5.

Sum of 9: (3,6), (4,5), (5,4), (6,3) → 4.

Total favorable: 5 + 4 = 9.

Total possible: 6*6 = 36.

Probability: 9/36 = 1/4. So the answer is 1/4.

Answer:

The option with \( \boldsymbol{\frac{1}{4}} \) (the last option, e.g., if the last option is labeled with 1/4, then that's the answer).