Three coins are tossed; what is the probability that two are...

Name: Problem 2, Chapter 16: Mathematical Methods in the Physical Sciences
Uploaded: 2022-01-07T17:26:23-08:00
Duration: 3 min 19 s
Channel: Raj Bala
Description: Three coins are tossed; what is the probability that two are heads and one tails? That the first two are heads and the third tails? If at least two are heads, what is the probability that all are heads?

Three coins are tossed; what is the probability that two are heads and one tails? That the first two are heads and the third tails? If at least two are heads, what is the probability that all are heads?

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Key Concepts

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. For coin tosses, it involves listing all combinations of heads and tails that can occur, which forms the basis for determining probabilities of various events.

Equally Likely Outcomes

This concept means that, in an experiment such as coin tossing, each outcome in the sample space has the same chance of occurring. This assumption allows us to calculate probabilities by counting the favorable outcomes and dividing by the total number of outcomes.

Counting Techniques

Counting techniques involve methods like listing, combinations, or permutations to determine the number of ways certain events can occur. These techniques are crucial in computing probabilities, particularly when the events involve specific counts of heads and tails.

Conditional Probability

Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. This concept is essential when the probability of one event depends on the occurrence of another, as in the case of determining the probability of all coins being heads given that at least two are heads.

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