Question

A hungry' undergraduate student was looking for a way of making some extra money. The student turned to a life of vice - gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following questions assuming no card replacement occurs and each section is independent of the previous sections (i.e., part b is independent of part a). As a reminder, there are 52 cards in a deck and four suits (hearts, diamonds, spades, and clubs). Please show your answers in fraction form and then solve to four decimal places. Make sure to show your work by typing out your work directly into the answer box. You may use the answer box to type work as well as the equation editor, but d do not copy and paste anything. For example, if you wanted to show that the average of 1, 2, and 3 was 2 you could type average 1. What is the probability that the student would get an ace, king, queen, jack and 10 in that order? 2. What is the probability that the second card drawn is a heart given that the first card drawn was a heart? 3. What is the probability that the student would get two aces on the first two cards drawn? 4. What is the probability that the student would draw a queen or a heart on the first draw? HTML Editort Paragraph

Answer 1

1.

P(A, K, Q, J, 10) =(4/52)(4/51)(4/50)(4/49)(4/48) =20/311875200 =0.0000

2.

Let, drawing heart on first draw =H1 and drawing heart on second draw is H2.

P(H2/H1) =P(H1.H2)/P(H1) =(13/52)(12/51)/(13/52) =12/51 =0.2353

or simply, P(H2/H1) =P(H2) since, two are independent draws. Thus, P(H2/H1) =P(H2) =12/51 =0.2353

3.

P(AA) =(4/52)(3/51) =12/2652 =0.0045

4.

P(Q or H) =4/52 + 13/52 =17/52 =0.3269