Unit 4: Probability, Random Variables and Distributions

In a large high school, 60% of students play a sport ([math]), 40% participate in a club ([math]), and 25% do both.

A game costs [math]10 if you roll a 6, $3 if you roll a 4 or 5, and nothing if you roll 1, 2, or 3.

A medical test for a rare disease has a 98% sensitivity (true positive rate) and a 95% specificity (true negative rate). The disease affects 0.5% of the population.

A manufacturer reports that 12% of its widgets are defective. A quality inspector randomly selects 20 widgets from a large production run.

A basketball player makes free throws with probability 0.80. She shoots free throws until she misses.

Let [math] represent the score on a math quiz with [math] and [math]. Let [math] represent the score on a science quiz with [math] and [math]. The scores are independent.

A survey of 500 adults produced the following table of exercise habits and diet type:

An insurance company sells a one-year term life insurance policy to a 40-year-old man for [math]100,000.

At a university, 35% of students are in STEM majors ([math]), 20% are student-athletes ([math]), and 8% are both STEM and student-athletes.

In a cereal promotion, each box contains one of 5 different toys, distributed equally. A child wants to collect all 5 toys.