A basketball player s\ucceeds in making a basket 3 tries out of 4 . How many tries are necessary

step 1 In this question we are given that the probability of making a basket for a player is equal to t

A basketball player s\ucceeds in making a basket 3 tries out...

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Key Concepts

Bernoulli Trials

A Bernoulli trial is an experiment where there are only two possible outcomes, typically termed 'success' and 'failure'. In this context, each basketball shot is a Bernoulli trial because the shot can either be a basket (success) or not (failure), with a fixed probability for success.

Complement Rule

The complement rule states that the probability of an event occurring is one minus the probability of it not occurring. When determining the probability of at least one success in repeated independent trials, it is often easier to calculate the probability of no successes and then subtract that value from one.

Exponential Inequality

Exponential inequalities arise when the probability of an event not occurring is raised to the power of the number of trials. To determine the number of trials needed for a certain overall probability threshold, the inequality is set up in terms of an exponent and then solved to find the minimum number of trials required.

Logarithms

Logarithms are a mathematical tool used to solve equations where the unknown variable appears in an exponent. When solving for the number of trials in an exponential inequality, logarithms allow one to isolate the exponent and determine the precise number of required trials.

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