A coin is tossed 2 times. What is the probability of getting all heads? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
Answer (2)
The probability of getting all heads when tossing a coin twice is 4 1 or 0.250. This is calculated by multiplying the probability of heads for each independent toss. Therefore, the final answer is 4 1 or 0.250.
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The probability of getting a head in one coin toss is 2 1 .
The probability of getting heads in two independent coin tosses is the product of the probabilities of getting a head in each toss.
Calculate the probability: 2 1 × 2 1 = 4 1 .
Convert to decimal and round to three decimal places: 0.250 .
Explanation
Understand the problem When a coin is tossed, there are two possible outcomes: heads (H) or tails (T). The probability of getting a head in a single toss is 2 1 , and the probability of getting a tail is also 2 1 . We are tossing the coin 2 times, and we want to find the probability of getting heads in both tosses.
Independent events Since the two coin tosses are independent events, the probability of getting heads in both tosses is the product of the probabilities of getting a head in each toss.
Calculate the probability The probability of getting a head in the first toss is 2 1 . The probability of getting a head in the second toss is also 2 1 . Therefore, the probability of getting heads in both tosses is: 2 1 × 2 1 = 4 1
Convert to decimal To express the answer as a decimal number rounded to three decimal places, we convert the fraction 4 1 to a decimal: 4 1 = 0.25 Rounding to three decimal places, we get 0.250 .
Final Answer The probability of getting all heads when a coin is tossed 2 times is 4 1 or 0.250 .
Examples
Imagine you're playing a game where you need to flip two heads in a row to win a prize. Knowing the probability of getting two heads helps you understand your chances of winning. In this case, there's a 1 in 4 chance, or 25%, that you'll flip two heads in a row.
