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Problem 1

# Find the probability of the given event. The coin lands heads all five times.

Expert verified
The probability of the coin landing heads all five times is $$1/32$$ or approximately 0.03125.
See the step by step solution

## Step 1: Identify the probability of a single toss

First, we need to determine the probability of the coin landing heads in a single toss. For a fair coin, there are two possible outcomes: heads and tails. Both outcomes have an equal chance of happening, so the probability of getting heads is 1/2 (one out of two possible outcomes).

## Step 2: Use the multiplication rule for independent events

Since the coin tosses are independent events, we can use the multiplication rule to find the probability of getting heads all five times. This rule states that the probability of multiple independent events occurring is the product of their individual probabilities. In this case: P(getting heads all 5 times) = P(getting heads in the 1st toss) × P(getting heads in the 2nd toss) × P(getting heads in the 3rd toss) × P(getting heads in the 4th toss) × P(getting heads in the 5th toss)

## Step 3: Calculate the probability

Using the probability of getting heads in a single toss (1/2) and applying the multiplication rule, we can now calculate the probability of getting heads all five times: P(getting heads all 5 times) = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = (1/2)^5 = 1/32 So the probability of the coin landing heads all five times is 1/32 or approximately 0.03125.

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