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Math  /  Data & Statistics

Question3. If two coins are flipped, what is the probability of getting at least one head?

Studdy Solution

STEP 1

Assumptions
1. We are flipping two fair coins.
2. Each coin has two possible outcomes: heads (H) or tails (T).
3. The probability of getting heads on a single coin flip is 12 \frac{1}{2} .
4. The probability of getting tails on a single coin flip is 12 \frac{1}{2} .
5. We are looking for the probability of getting at least one head in the two flips.

STEP 2

List all possible outcomes when two coins are flipped. Each coin can be either heads (H) or tails (T), so the possible outcomes are:
1. HH (both coins are heads)
2. HT (first coin is heads, second coin is tails)
3. TH (first coin is tails, second coin is heads)
4. TT (both coins are tails)

STEP 3

Calculate the total number of possible outcomes. Since each coin has 2 possible outcomes and we have 2 coins, the total number of outcomes is:
2×2=4 2 \times 2 = 4

STEP 4

Identify the favorable outcomes for getting at least one head. The favorable outcomes are:
1. HH
2. HT
3. TH

STEP 5

Count the number of favorable outcomes. There are 3 favorable outcomes: HH, HT, and TH.

STEP 6

Calculate the probability of getting at least one head. The probability is the number of favorable outcomes divided by the total number of possible outcomes:
P(at least one head)=Number of favorable outcomesTotal number of outcomes=34 P(\text{at least one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{4}
The probability of getting at least one head when two coins are flipped is 34 \frac{3}{4} .

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