Question

1. ben rolls two number cubes. what is the probability that the sum of the numbers he rolls is less than 6?
2. nhan is getting dressed. he considers two different shirts, three pairs of pants, and three pairs of shoes. he chooses one of each of the articles at random. what is the probability that he will wear his jeans but not his sneakers?

shirt	pants	shoes
collared	khakis	sneakers
t - shirt	jeans	flip - flops
	shorts	sandals

Explanation:

Question 14

Step1: Find total outcomes

When rolling two number cubes (each with 6 faces), total outcomes = \(6\times6 = 36\).

Step2: Find favorable outcomes (sum < 6)

Possible pairs \((a,b)\) where \(a + b<6\):

• Sum = 2: (1,1) → 1 outcome
• Sum = 3: (1,2), (2,1) → 2 outcomes
• Sum = 4: (1,3), (2,2), (3,1) → 3 outcomes
• Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 outcomes

Total favorable = \(1 + 2 + 3 + 4 = 10\).

Step3: Calculate probability

Probability = \(\frac{\text{favorable}}{\text{total}}=\frac{10}{36}=\frac{5}{18}\).

Step1: Total number of combinations

Shirts: 2 (collared, T - shirt), Pants: 3 (khakis, jeans, shorts), Shoes: 3 (sneakers, flip - flops, sandals). Total combinations = \(2\times3\times3 = 18\).

Step2: Favorable combinations (jeans, not sneakers)

• Shirts: 2 choices (collared, T - shirt)
• Pants: 1 choice (jeans)
• Shoes: 2 choices (flip - flops, sandals)

Favorable combinations = \(2\times1\times2 = 4\).

Step3: Calculate probability

Probability=\(\frac{4}{18}=\frac{2}{9}\).

Answer:

\(\frac{5}{18}\)

Question 15