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Suppose you toss a coin three times and count the number of tails. Fill in the blanks in the following table to create a probability model for this situation. Give all probabilities as a fraction or a number between 0 and 1.Group of answer choices0 tails: 28, 1 tail: 28, 2 tails: 38, 4 tails: 180 tails: 08, 1 tail: 28, 2 tails: 28, 4 tails: 180 tails: 18, 1 tail: 38, 2 tails: 38, 3 tails: 18

Question

Suppose you toss a coin three times and count the number of tails. Fill in the blanks in the following table to create a probability model for this situation. Give all probabilities as a fraction or a number between 0 and 1.Group of answer choices0 tails: 28, 1 tail: 28, 2 tails: 38, 4 tails: 180 tails: 08, 1 tail: 28, 2 tails: 28, 4 tails: 180 tails: 18, 1 tail: 38, 2 tails: 38, 3 tails: 18

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Solution

To solve this problem, we need to determine the probability of getting 0, 1, 2, or 3 tails when tossing a coin three times. Let's start by listing all possible outcomes of tossing a coin three times:

  1. HHH
  2. HHT
  3. HTH
  4. HTT
  5. THH
  6. THT
  7. TTH
  8. TTT

There are 8 possible outcomes in total. Now, let's count the number of tails in each outcome:

  1. HHH - 0 tails
  2. HHT - 1 tail
  3. HTH - 1 tail
  4. HTT - 2 tails
  5. THH - 1 tail
  6. THT - 2 tails
  7. TTH - 2 tails
  8. TTT - 3 tails

Next, we count the number of outcomes for each number of tails:

  • 0 tails: 1 outcome (HHH)
  • 1 tail: 3 outcomes (HHT, HTH, THH)
  • 2 tails: 3 outcomes (HTT, THT, TTH)
  • 3 tails: 1 outcome (TTT)

Now, we calculate the probability for each number of tails by dividing the number of outcomes by the total number of possible outcomes (8):

  • 0 tails: 1/8
  • 1 tail: 3/8
  • 2 tails: 3/8
  • 3 tails: 1/8

So, the completed probability model is:

  • 0 tails: 1/8
  • 1 tail: 3/8
  • 2 tails: 3/8
  • 3 tails: 1/8

This problem has been solved

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