Question

for each game, determine the sample space using a list or tree diagram. then determine the indicated probability. (examples 3 - 4)

1. alana tosses 2 number cubes. she wins if she rolls double sixes.

determine p(alana wins).

1. ming rolls a number cube, tosses a coin, and chooses a card from two cards marked a and b. if an even number and heads appears, ming wins, no matter which card is chosen. otherwise lashonda wins. determine p(ming wins).

Explanation:

Problem 5

Step 1: Determine Sample Space

A number cube has 6 faces (1 - 6). Tossing 2 number cubes, the sample space has \(6\times6 = 36\) outcomes (each of the 6 outcomes of the first cube pairs with each of the 6 of the second).

Step 2: Identify Favorable Outcomes

"Double sixes" means both cubes show 6, so there's 1 favorable outcome: \((6,6)\).

Step 3: Calculate Probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{36}\).

Step 1: Determine Sample Space Sizes

• Number cube: 6 outcomes (1 - 6).
• Coin: 2 outcomes (Heads, Tails).
• Cards: 2 outcomes (A, B).

Total outcomes: \(6\times2\times2 = 24\).

Step 2: Identify Favorable Outcomes

• Even numbers on cube: 2, 4, 6 (3 outcomes).
• Heads on coin: 1 outcome.
• Cards: 2 outcomes (any card is fine).

Favorable outcomes: \(3\times1\times2 = 6\).

Step 3: Calculate Probability

\(P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}=\frac{6}{24}=\frac{1}{4}\).

Answer:

\(\frac{1}{36}\)

Problem 6