Question

(g) prime number on one or both dice
when rolling two dice, the probability of rolling a prime number on one or both dice is

part 8 of 8
(h) sum greater than 1
when rolling two dice, the probability of rolling a sum greater than 1 is

Explanation:

Step1: Calculate total outcomes

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

Step2: Calculate non - prime outcomes

The non - prime numbers on a die (\(1,4,6\)). The number of non - prime outcomes for one die is 3. The number of outcomes where both dice show non - prime numbers is \(n(\text{non - prime on both})=3\times3=9\)

Step3: Calculate probability using complement rule

Let \(A\) be the event of getting a prime number on one or both dice. Using the complement rule \(P(A)=1 - P(\text{non - prime on both})\)
\(P(A)=1-\frac{9}{36}=\frac{36 - 9}{36}=\frac{27}{36}=\frac{3}{4}\)

For part (h):

Step1: Analyze the sum of two dice

The minimum sum when rolling two dice is \(1 + 1=2\). Since \(2>1\), all possible outcomes of rolling two dice result in a sum greater than 1.

Step2: Calculate probability

The probability \(P=\frac{n(\text{favorable})}{n(S)}\). Here, \(n(\text{favorable}) = 36\) and \(n(S)=36\). So \(P = 1\)

Answer:

(g) \(\frac{3}{4}\)
(h) \(1\)