You are dealt 5 cards from a standard 52 card deck. What is the probability that you are dealt a “four of a kind” in ace ?

(52장의 카드에서 5장을 받았을 때 "에이스 포카"가 될 확률은?)

다양한 문서 작성/편집 S/W에서 쓰이는 Style/서식/Template 등의 기능에 대해 알고 있는가? 활용하는가?

The Conditional Probability : $$\Pr\left(A\mid B\right)\ =$$  

(Be careful, there can be more than one correct answer. Full points are awarded only if all correct answers are selected)

Mr. B, Mr. C and Mr. D are land owners of a county called "U" and they are owning 1/2, 1/3 and 1/6 of the land of the county "U" respectively. Mr. A purchases 1/3 of the Mr. B's land, 1/6 of the Mr. C's land and 1/2 of the Mr. D's land.

How much, in percent, of the land of "U" is purchased by Mr. A?

Mr. B, Mr. C and Mr. D are land owners of a county called "U" and they are owning 1/2, 1/3 and 1/6 of the land of the county "U" respectively. Mr. A purchases 1/3 of the Mr. B's land, 1/6 of the Mr. C's land and 1/2 of the Mr. D's land.

How much, in percent, of the land of "A" is originally owned by Mr. D?

In the Auditorium Example in the lecture material,

Find the probability that Seat 15 was selected given that Row 20 was selected.

$$\Pr\left(S=15\mid R=20\right)=$$  

In the Auditorium Example in the lecture material,

Find the probability that Seat 15 was selected.

$$\Pr\left(S=15\right)\approx$$  

In the Auditorium Example in the lecture material,

Find the probability that Row 20 was selected given that Seat 15 was selected.

$$\Pr\left(R=20\mid S=15\right)\approx$$  

Medical Test Example

You’ve got some medical tests. The results turned out that you tested positive for a very rare disease that is known to affect about 0.1% of the population. It is a nasty disease with horrible consequences.

You asked your doctor “How certain is it that I have this disease ?”. The doctor says that the test correctly identify 99% of people that have the disease and only incorrectly identify 1% of people who don’t have the disease.

What are the chances that you actually have this disease ?

PMF의 정의로 적합한 것은?

확률이 p인 Bernoulli 시행을 n번 시행하는 Binomial Random Variable의 평균은?

확률이 p인 Bernoulli 시행을 해당 Event가 발생하지 않을 때까지 반복하여 수행하는 Geometric Random Variable의 평균은 ?

Alice, Bob, and Carol take turns flipping a fair coin, and the winner is the first player to flip a head. If Alice flips the coin first, what is the probability that Alice wins?

Suppose the arrival of telephone calls at a switch can be modeled with Poisson. That is, if 𝑋 is the number of calls that arrives in 𝑡 minutes, then

$$P_X\left(k\right)=\frac{\left(\lambda\cdot t\right)^k}{k!}e^{-\lambda t}$$  

$$\lambda$$  is the average arrival rate in calls/minute. Suppose that the average rate of calls is 10 per minute

What is the probability that fewer than three calls will be received in the first 6 seconds ?

Suppose the arrival of telephone calls at a switch can be modeled with Poisson. That is, if 𝑋 is the number of calls that arrives in 𝑡 minutes, then

$$P_X\left(k\right)=\frac{\left(\lambda\cdot t\right)^k}{k!}e^{-\lambda t}$$  

$$\lambda$$  is the average arrival rate in calls/minute. Suppose that the average rate of calls is 10 per minute

What is the probability that fewer than three calls will be received in the first 6 minutes ?