In a lot of 50 light bulbs, there are 2 bad bulbs. An...

In a lot of 50 light bulbs, there are 2 bad bulbs. An inspector examines five bulbs, which are selected at random and without replacement. (a) Find the probability of at least one defective bulb among the five. (b) How many bulbs should be examined so that the probability of finding at least one bad bulb exceeds $\frac{1}{2}$ ?

In a lot of 50 light bulbs, there are 2 bad bulbs. An inspector examines five bulbs, which are selected at random and without replacement.
(a) Find the probability of at least one defective bulb among the five.
(b) How many bulbs should be examined so that the probability of finding at least one bad bulb exceeds $\frac{1}{2}$ ?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Hypergeometric Distribution

This concept describes the probability of drawing a certain number of successes from a finite population without replacement. It is used in situations where the sampled items are taken from groups with known numbers of successes and failures, allowing for the determination of probabilities based on combinatorial counts.

Complementary Probability

This concept involves calculating the probability of an event by subtracting the probability of the event's complement from one. It is especially useful when the direct computation of an event is complex, while its complement is simpler to compute.

Combinatorial Analysis

This concept involves the use of combinations and counting methods to determine the number of ways events can occur. It is essential in probability problems where items are selected from a set, particularly in contexts with multiple outcomes under selection without replacement.

Probability Thresholds

This concept deals with determining the minimum number of trials or selections needed to exceed a given probability level for an event. It often involves setting up and solving inequalities to find when the cumulative probability of success surpasses a specified threshold.

Transcript

Please give Ace some feedback