Understanding Binomial Distribution through Free Throws

The video tutorial explores the concept of binomial distribution through a scenario of making free throws. It defines a random variable X as the number of successful shots out of six attempts, assuming a 70% success rate. The tutorial calculates the probabilities for different values of X, from zero to six successful shots, and explains the lack of symmetry in the distribution due to the higher likelihood of making a shot. The symmetry is instead found in the binomial coefficients. The video encourages plotting the distribution for better visualization.

What is the random variable X defined as in the context of the free throw scenario?

• The number of successful free throws out of six

• The number of attempts made

• The total number of free throws missed

• The probability of making a single free throw

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What is the probability of making zero free throws out of six attempts?

• Approximately 5%

• Approximately 1%

• Approximately 10%

• Approximately 0.1%

How does the probability of making one free throw compare to making zero free throws?

• It is ten times more likely

• It is the same

• It is half as likely

• It is twice as likely

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What is the approximate probability of making two free throws?

• 10%

• 15%

• 6%

• 1%

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What is the probability of making three free throws out of six?

• 5.5%

• 18.5%

• 10.5%

• 25.5%

What is the probability of making exactly four free throws?

• 42.4%

• 22.4%

• 32.4%

• 12.4%

What is the probability of making five free throws?

• 40.3%

• 30.3%

• 20.3%

• 10.3%

What is the probability of making all six free throws?

• 11.8%

• 21.8%

• 41.8%

• 31.8%

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Why is there no symmetry in the probability distribution of making free throws?

• Because the number of attempts is odd

• Because the probability of making a shot is higher than missing

• Because the probability of missing is higher than making

• Because the distribution is not binomial

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What would cause the probability distribution to be symmetric?

• If the number of attempts were decreased

• If the probability of making a shot were 0.8

• If the probability of making and missing were both 0.5

• If the number of attempts were increased

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