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 .
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:
Expressing this as a decimal:
Thus, the probability that the sequence of tosses is TTTT is .
Would you like any further details on this problem?
Here are 5 related questions:
- What is the probability of getting exactly two tails in four coin tosses?
- How many possible outcomes are there when a coin is tossed four times?
- What is the probability of getting at least one head in four tosses?
- If the coin is biased with a 60% chance of landing heads, what is the probability of TTTT?
- What is the probability of getting the sequence HHTT?
Tip: When calculating probabilities for independent events, multiply the individual probabilities of each event.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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