Que.Three coins are tossed together. Find the probability of getting: (a) exactly two heads. (b) at least two tails. (c) at most one head.

视频信息

答案文本 复制

视频字幕 复制

Let's solve this step by step. When three coins are tossed together, we need to find the sample space first. Each coin can show either heads or tails, giving us 8 possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. For part a, we need exactly two heads. Looking at our sample space, the favorable outcomes are HHT, HTH, and THH. That's 3 outcomes out of 8 total outcomes. Therefore, the probability of getting exactly two heads is 3 divided by 8. For part b, we need at least two tails, which means two or three tails. The favorable outcomes are HTT, THT, TTH, and TTT. That's 4 outcomes out of 8 total outcomes. Therefore, the probability is 4 divided by 8, which simplifies to 1 half. For part c, we need at most one head, which means zero or one head. The favorable outcomes are TTT with zero heads, and HTT, THT, TTH with one head each. That's 4 outcomes out of 8 total outcomes. Therefore, the probability is 4 divided by 8, which simplifies to 1 half. To summarize our results: For part a, the probability of exactly two heads is 3 over 8. For part b, the probability of at least two tails is 1 half. For part c, the probability of at most one head is also 1 half. The key method is to identify the sample space, count favorable outcomes, and apply the probability formula.