In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting two heads.

검증된 단계별 안내

Identify the sample space for tossing a fair coin two times. The sample space consists of all possible outcomes: \(\{HH, HT, TH, TT\}\).

Count the total number of outcomes in the sample space. Since there are two tosses and each toss has 2 possible outcomes, the total number of outcomes is 4.

Determine the favorable outcomes for the event 'getting two heads'. This means both tosses result in heads, so the favorable outcome is \(\{HH\}\).

Count the number of favorable outcomes. Here, there is only 1 favorable outcome: \(HH\).

Calculate the probability of getting two heads using the formula: \(P(\text{two heads}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{1}{4}\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sample Space

The sample space is the set of all possible outcomes of an experiment. For tossing a fair coin twice, the sample space includes {HH, HT, TH, TT}, representing all equally likely sequences of heads (H) and tails (T). Understanding the sample space is essential for calculating probabilities.

Probability of an Event

Probability measures the likelihood of an event occurring and is calculated as the ratio of favorable outcomes to the total number of outcomes in the sample space. For example, the probability of getting two heads is the number of outcomes with two heads divided by the total outcomes.

Equally Likely Outcomes

When all outcomes in the sample space have the same chance of occurring, they are called equally likely. This assumption allows us to use simple ratios to find probabilities, such as dividing the count of favorable outcomes by the total number of outcomes.