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Chapter 9: Problem 560

Find the probability that a person flipping a balanced coin requires four tosses to get a head.

Short Answer

Expert verified
The probability that a person flipping a balanced coin requires four tosses to get their first head is \(1/16\).

Step by step solution

01

Determine the probability of each toss

Since the coin is balanced, the probabilities for getting a head (H) or a tail (T) in each toss are equal and independent of each other. Therefore, the probability of getting a head in any toss is P(H) = 1/2, and the probability of getting a tail in any toss is P(T) = 1/2.
02

Calculate the probability of the desired sequence

The desired sequence in this case is TTT H, which means getting three tails and then a head. Since the events are independent, the probability of this sequence is the product of the probabilities of each event: P(TTT H) = P(T) * P(T) * P(T) * P(H).
03

Substitute the probabilities of each event

Now we will substitute the probabilities of each event in the formula calculated in Step 2. P(T) = 1/2 and P(H) = 1/2, so the probability of the sequence TTT H is: P(TTT H) = (1/2) * (1/2) * (1/2) * (1/2).
04

Simplify the expression and find the probability

Simplify the expression by multiplying the fractions together: P(TTT H) = (\(1/2\))^4 = 1/16. The probability that a person flipping a balanced coin requires four tosses to get their first head is 1/16.

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