Explanation
1. Calculate Total Sample Space (n(S)):
When rolling four six-sided dice, each die has 6 possible outcomes. Since the dice are independent, the total number of outcomes is:
n(S)=64=1296
2. Condition for "At Least 23":
The maximum possible sum with four dice is 6+6+6+6=24.
Therefore, "at least 23" implies the total sum is either 23 or 24.
Case 1: Total Sum = 24
The only combination is {6,6,6,6}.
Number of arrangements =1 way.
Case 2: Total Sum = 23
The only combination of digits is {6,6,6,5}.
The number of distinct arrangements of these digits is calculated as:
3!1!4!=4 ways
3. Calculate Total Favorable Outcomes (n(E)):
n(E)=1+4=5
4. Final Probability Calculation:
The probability P is the ratio of favorable outcomes to the total number of outcomes:
P=n(S)n(E)=12965
Correct Option:
(d) 12965
