Question

for the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 4 or greater than 6. the probability that the sum will be less than 4 or greater than 6 is (type an integer or a simplified fraction.)

Explanation:

Step1: Find total outcomes

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

Step2: Find sum < 4 outcomes

Sums less than 4: (1,1), (1,2), (2,1). So 3 outcomes.

Step3: Find sum > 6 outcomes

Sums greater than 6:
Sum = 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6
Sum = 8: (2,6),(3,5),(4,4),(5,3),(6,2) → 5
Sum = 9: (3,6),(4,5),(5,4),(6,3) → 4
Sum = 10: (4,6),(5,5),(6,4) → 3
Sum = 11: (5,6),(6,5) → 2
Sum = 12: (6,6) → 1
Total for sum > 6: \(6 + 5+4 + 3+2 + 1=21\)

Step4: Find total favorable

Favorable (sum < 4 or sum > 6) = 3 + 21 = 24

Step5: Calculate probability

Probability = \(\frac{24}{36}=\frac{2}{3}\)

Answer:

\(\frac{2}{3}\)