An experiment consists of tossing a fair coin twice. The student reasons that there are three possible outcomes: two heads, one head and one tail, or two tails. Thus,P(HH) 1/3
HH
TT
TH
HT
Four possibilities.
The student's reasoning is incorrect. To determine the probability of an event, we need to consider the number of favorable outcomes over the total number of possible outcomes.
In this experiment, the total number of possible outcomes when tossing a fair coin twice is 2 * 2 = 4. Each coin has two possible outcomes, and since there are two coins, the total number of outcomes is 2 * 2 = 4.
Now let's determine the favorable outcomes for getting two heads (HH). There is only one way to get two heads, which is HH.
Therefore, the probability of getting two heads (HH) is 1 out of 4, or 1/4.
To determine the probability of getting two heads in a row (HH) when tossing a fair coin twice, we need to first understand the total number of possible outcomes.
When tossing a coin twice, each coin has two possible outcomes – heads (H) or tails (T). Since we are tossing the coin twice, the total number of outcomes is the product of the number of outcomes for each coin toss. For each toss, there are two possibilities – heads or tails. Therefore, there are 2 * 2 = 4 possible outcomes for tossing a coin twice.
The four possible outcomes are: HH, HT, TH, and TT.
Now, we can determine the probability of getting two heads (HH). Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes.
In this case, we have one desired outcome (HH) out of four possible outcomes (HH, HT, TH, and TT). So, the probability of getting two heads is 1/4, not 1/3 as initially stated.
To summarize, the correct probability of getting two heads (HH) when tossing a fair coin twice is 1/4.