It All Boils Down to a Set Number of Types of Problems

It all boils down to a set number of types of problems:

Binomial Formulas

If they ask for the probability of EXACTLY a set number of successes out of a fixed number of attempts:

Examples:

What is the probability that Corinne will hit exactly 8 of her next 16 shots?

What is the probability that Corinne will hit half of her next 16 shots?

If they ask for the probability of (AT MOST, A SET NUMBER OR LESS) number of successes out of a fixednumber of attempts:

Examples:

What is the probability that Corinne will hit at most 7 of her next 16 shots?

What is the probability that Corinne will hit 7 or fewer of her next 16 shots?

What is the probability that Corinne will hit no more than 7 of her next 16 shots?

If they ask for the probability of (AT LEAST, A SET NUMBER OR MORE) number of successes out of a fixed number of attempts:

Examples:

What is the probability that Corinne will hit at least 7 of her next 16 shots?

What is the probability that Corinne will hit 7 or more of her next 16 shots?

What is the probability that Corinne will hit no less than 7 of her next 16 shots?

… Then this translates into hitting more than 6 …

What is the probability that Corinne will hit more than 7 of her next 16 shots?

How do I get an average/mean (”Expected Value”) and a standard deviation?

Geometric Formulas

If they ask for the probability of it taking EXACTLY a set number of attempts to achieve the first success.

Example:

What is the probability that it will take Corinne exactly 8 shots to finally hit a shot?

If they ask for the probability of it taking (AT MOST, A SET NUMBER OR LESS) a set number of attempts to achieve the first success.

Examples:

What is the probability that it will take Corinne at most 7 attempts before she makes her first successful shot?

What is the probability that it will take Corinne 7 or fewer attempts before she makes her first successful shot?

What is the probability that it will take Corinne no more than 7 attempts before making her first shot?

If they ask for the probability of it taking (AT LEAST, A SET NUMBER OR MORE) number of attempts before we observe the first success:

* Special Formula *

What is the probability that it will take Corinne at least 7 attempts make her first shot?

What is the probability that it will take Corinne 7 or more attempts make her first shot?

What is the probability that it will take Corinne no less than 7 attempts make her first shot?

… Then they translate into it taking more than 6 …

How do I get an average and a standard deviation?