Question

NO LINKS!! URGENT HELP PLEASE!!

You are making a sandwich to take for lunch. You can choose between white bread or wheat bread, which both have a 50% chance of being selected. Then choose your main topping. There's a 30% you would choose ham, 25% that you choose turkey, and 45% that you make PB and J instead. Unfortunately, you only have American cheese, so your final option you can choose American cheese (65%), or no cheese at all (35%). Make a tree diagram. What is the probability that you choose a ham sandwich with American cheese, or PB and J (without cheese)?

Answer 1

Ham Sandwich with American cheese = 0.015

PB and J without cheese = 0.1575

Both probabilities together = 0.1725

Explanation:

Attached is the tree diagram

Hope this helped

Answer 2

The probability that you would choose to make a ham sandwich with American cheese OR a PB and J sandwich without cheese is 35.25%.

Explanation:

Tree diagrams show the probabilities for a sequence of two or more independent events.

For the given problem:

• Event 1 is the choice of of bread.
• Event 2 is the choice of main topping.
• Event 3 is the choice of cheese or no cheese.

These events are independent events since each event is not affected by the previous event.

The given probabilities for each choice are:

• White bread = 50%
• Wheat bread = 50%
• Ham = 30%
• Turkey = 25%
• PB and J = 45%
• Cheese = 65%
• No cheese = 100% - 65% = 35%

Create a tree diagram with the given information (see attachment 1).

The end of each branch should be labelled with its outcome, and the probability of that event should be written along the branch.

To calculate the probability of each combination, multiply the probabilities along the branches.

To find the probability that you would choose to make a sandwich with white bread, ham and cheese, multiply along the branches representing those events:

⇒ 50% × 30% × 65% = 9.75%

To find the probability that you would choose to make a sandwich with wheat bread, ham and cheese, multiply along the branches representing those events:

⇒ 50% × 30% × 65% = 9.75%

To find the probability that you would choose to make a sandwich with white bread, PB & J and no cheese, multiply along the branches representing those events:

⇒ 50% × 45% × 35% = 7.875%

To find the probability that you would choose to make a sandwich with wheat bread, PB & J and no cheese, multiply along the branches representing those events:

⇒ 50% × 45% × 35% = 7.875%

On a tree diagram, when moving along the branches (from left to right) we multiply, and when moving down we add.

Therefore, to calculate the probability that you would choose to make a ham sandwich with American cheese, or a PB and J sandwich without cheese, add the four found probabilities:

⇒ 9.75% + 9.75% + 7.875% + 7.875% = 35.25%