Problem 2. Die roll experiment In an experiment, die is rolled continually until

Question

Problem 2. Die roll experiment In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops. (a) (5 points) What is the sample space of this experiment? (b) (5 points)Let En denote the event thatnlls are necessary to complete the experiment. How can you describe the event (UEn)? Problem 3. Seating chart many ways can 8 people be seated in a row if (a) (5 points) There are no restrictions on the seating arrangement? (b) (5 points) Persons A and B don't want to seat together? (c) (5 points) There are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (d) (5 points) There are 4 married couples and each couple must sit together? Problem 4. Poker hands Each hand in Poker consists of 5-cards from a deck of 52 cards (4 suits and 13 ranks). The most common hands are one pair and two-pair: One-pair: Two cards of one rank, plus three cards which are not of this rank nor the same as each other, such as {4% ,4, K+,10+, 5. } Two-pair: Two cards of the same rank, plus two cards of another rank (that match each other but not the first pair), plus any card not of either rank; such as {J%)+. 4, 4., 9 (a) (5 points) How many 5-card poker hands are there? b) (10 points) What is the probability of getting one-pair in a 5-card poker hand? (c) (10 points) What is the probability of getting two-pair in a 5-card poker hand?

Explanation / Answer

Q3.

(a) If there is no restriction, then we can arrange 8 people on 8 seats as in 8! ways.

(b) Total ways = 8! = 40320. Combinations in which A and B dont sit together = Total combinations - combinations where A and B sit together.

We can choose 2 seats for A and B in 7 ways. Now, A and B can interchange their places, so total ways = 7*2 = 14

Answer = 40320 - 14 = 40306

(c) 4 men and 4 women: We can select the gender-wise combinations as either MWMWMWMW or WMWMWMWM.

We can place 4 men at 4 places in 4! ways and women in 4! ways.

So, total number of ways = 2*(4!*4!) = 1152

(d) 4 married couples and they want to sit together: Let the couples be C1, C2, C3, C4, where Ci represents MiWi.

Now we have 4 places and 4 couples. They can sit in 4! ways. Now Ci can be either MiWi or WiMi.

Total number of ways = 4!*2^4 = 384

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.