Question

(d) sum less than or equal to 11
when rolling two dice, the probability of rolling a sum less than or equal to 11 is
part 5 of 8

Explanation:

Step1: Calculate total number of outcomes

When rolling two dice, each die has 6 possible outcomes. By the fundamental counting principle, the total number of outcomes when rolling two dice is \(n(S)=6\times6 = 36\).

Step2: Calculate number of outcomes with sum greater than 11

The possible sums when rolling two dice range from \(2\) (\(1 + 1\)) to \(12\) (\(6+6\)). The sum greater than \(11\) is \(12\). There is only \(1\) way to get a sum of \(12\), which is \((6,6)\). Let \(A\) be the event of getting a sum greater than \(11\), so \(n(A) = 1\).

Step3: Calculate probability of complement event

Let \(B\) be the event of getting a sum less than or equal to \(11\). We know that \(P(B)=1 - P(A)\).
Since \(P(A)=\frac{n(A)}{n(S)}=\frac{1}{36}\), then \(P(B)=1-\frac{1}{36}=\frac{36 - 1}{36}=\frac{35}{36}\)

Answer:

\(\frac{35}{36}\)