The following items are in a cooler: one turkey sandwich, one ham sandwich, one bottle of soda, and one bottle of water. The sandwiches are the same size and same shape. The bottles are the same size and same shape. The tree diagram below shows all the possible combinations of randomly selecting one sandwich and one bottle. What is the probability of selecting a ham sandwich and a bottle of water?

Question

A 3/4
B 2/3
C 1/3
D 1/4

Answer 1

To find the probability of selecting a ham sandwich and a bottle of water, we first look at the possible combinations of selecting one sandwich and one bottle based on the items listed:

Items Available:

• Sandwiches: 1 Turkey, 1 Ham
• Bottles: 1 Soda, 1 Water

Possible Combinations:

1. Turkey Sandwich + Soda
2. Turkey Sandwich + Water
3. Ham Sandwich + Soda
4. Ham Sandwich + Water

So there are a total of 4 combinations possible.

Favorable Outcome: The favorable combination for selecting a ham sandwich and a bottle of water is:

• Ham Sandwich + Water

Thus, there is 1 favorable outcome.

Calculating Probability: The probability of an event can be calculated using the formula: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] In this case:

• Number of favorable outcomes = 1 (Ham Sandwich + Water)
• Total number of possible outcomes = 4

Substituting the values into the formula, we get: \[ \text{Probability} = \frac{1}{4} \]

Therefore, the probability of selecting a ham sandwich and a bottle of water is \( \frac{1}{4} \).

The answer is D 1/4.