Problem Solving Using Theoretical Probabilities Quick Check

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Question
Using the following information, make a prediction as to which event is most likely to occur.
A sandwich shop has 7 options for bread, 5 options for meat, 4 options for cheese, 10 options for toppings, and 6 options for dressing or sauce. Hera places an order for a sesame seed baguette with turkey, Swiss cheese, pickles, and mayonnaise. The person behind the counter randomly chooses one bread, 1 meat, 1 cheese, 1 topping, and 1 dressing.(1 point)
Responses

Hera gets the correct meat.
Hera gets the correct meat.

Hera gets the correct topping.
Hera gets the correct topping.

Hera gets the correct cheese.
Hera gets the correct cheese.

Hera gets the correct bread.

1 answer

To determine the most likely event to occur, we need to look at the total options available for each category (bread, meat, cheese, topping, and dressing) and compare them to the specific choices made by Hera.

  1. Bread options: 7
  2. Meat options: 5
  3. Cheese options: 4
  4. Topping options: 10
  5. Dressing options: 6

Hera ordered:

  • Bread: sesame seed baguette
  • Meat: turkey
  • Cheese: Swiss cheese
  • Topping: pickles
  • Dressing: mayonnaise

When the person behind the counter randomly chooses an option from each category, the probability of choosing Hera's specific option is as follows:

  • For bread: Probability = 1/7 (since there are 7 options)
  • For meat: Probability = 1/5 (since there are 5 options)
  • For cheese: Probability = 1/4 (since there are 4 options)
  • For topping: Probability = 1/10 (since there are 10 options)
  • For dressing: Probability = 1/6 (since there are 6 options)

Since Hera placed an order consisting of one of each category, we can now compare the probabilities of choosing the correct item for each category:

  • Bread: 1/7 (0.1429)
  • Meat: 1/5 (0.2)
  • Cheese: 1/4 (0.25)
  • Topping: 1/10 (0.1)
  • Dressing: 1/6 (0.1667)

Among these probabilities, the highest is for the cheese (1/4), which has the greatest likelihood of being the correct selection.

Conclusion: The most likely event to occur is that "Hera gets the correct cheese."