Math Problem Statement

A fair coin is tossed four times. What is the probability that the sequence of tosses is TTTT? Write your answer as a fraction or a decimal, rounded to four decimal places.

Solution

Each toss of a fair coin has two possible outcomes: heads (H) or tails (T). The probability of getting a tail (T) on any single toss is 12\frac{1}{2}.

Since the tosses are independent of each other, the probability of getting four tails in a row (TTTT) is the product of the probabilities for each individual toss. That is:

P(TTTT)=12×12×12×12=116P(TTTT) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{16}

Expressing this as a decimal:

116=0.0625\frac{1}{16} = 0.0625

Thus, the probability that the sequence of tosses is TTTT is 0.06250.0625.

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Here are 5 related questions:

  1. What is the probability of getting exactly two tails in four coin tosses?
  2. How many possible outcomes are there when a coin is tossed four times?
  3. What is the probability of getting at least one head in four tosses?
  4. If the coin is biased with a 60% chance of landing heads, what is the probability of TTTT?
  5. What is the probability of getting the sequence HHTT?

Tip: When calculating probabilities for independent events, multiply the individual probabilities of each event.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

P(TTTT) = (1/2) × (1/2) × (1/2) × (1/2) = 1/16

Theorems

Multiplication Rule for Independent Events

Suitable Grade Level

Grades 5-7