A coin is biased so that a head is three time:s as likely to occur as a tail. Find the expected

step 1 Here in this question we are given that the head is three times more likely to come up as compar

A coin is biased so that a head is three time:s as likely to...

Key Concepts

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. In the context of coin tosses, each toss is a Bernoulli trial. The binomial framework is particularly useful when calculating the probability and expected number of outcomes, such as tails, over multiple tosses.

Expected Value

The expected value is a key concept in probability and statistics that represents the long-term average result of an experiment repeated many times. It is calculated by multiplying each outcome by its corresponding probability and summing these products. When applied to a coin toss scenario, the expected value of tails would be computed based on the probability of landing on tails in each individual toss, multiplied by the number of tosses.

Probability Ratio

The probability ratio expresses the relative likelihood of two outcomes. When one outcome is described as occurring a certain multiple times as often as the other, this ratio can be used to determine the individual probabilities by ensuring that their sum equals one. This concept is fundamental in setting up accurate models for experiments involving biased events.

Biased Coin

A biased coin is one in which the two possible outcomes, typically heads and tails, do not have equal probabilities. Instead, one outcome occurs more frequently than the other according to a specified ratio, which changes the underlying probability distribution from a fair coin scenario.

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