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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?

1 answer

To find the probability of selecting a ham sandwich and a bottle of water from the cooler, we first need to determine the total number of possible combinations of sandwiches and bottles.

You have the following options:

  • Sandwiches: 1 turkey sandwich (T) and 1 ham sandwich (H)
  • Bottles: 1 bottle of soda (S) and 1 bottle of water (W)

The possible combinations are:

  1. Turkey sandwich and soda (T, S)
  2. Turkey sandwich and water (T, W)
  3. Ham sandwich and soda (H, S)
  4. Ham sandwich and water (H, W)

This results in a total of 4 combinations.

Now, we are interested in the specific combination of a ham sandwich and a bottle of water (H, W). There is 1 favorable outcome (H, W) out of 4 possible combinations.

To find the probability of this event, we can use the formula:

\[ P(\text{H and W}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{4} \]

Thus, the probability of selecting a ham sandwich and a bottle of water is:

\[ \frac{1}{4} \text{ or } 0.25 \]