Question

In: Statistics and Probability

In the Clue game, A,B,C,D,E,F have to guess how Mr Bobby was murdered by drawing cards...

In the Clue game, A,B,C,D,E,F have to guess how Mr Bobby was murdered by drawing cards all different. There is 9 "pieces"; 6 "characters"; 6 "weapons".

We randomly draw a card from each pile, then place them in an envelope. The object of the game is to determine which combination of cards is in the envelope. 18 remaining cards are divided equally between the 6 players; each player: 3 cards

Q1. We haven't divided the cards yet.

(a) Suppose A had to guess the crime now. What would be the probability that his choice be the right one?

(b) Suppose A will have to guess the crime immediately after seeing his three cards. What would be the different options and their probability knowing the 18 remaining cards are divided equally between the 6 players.

Q2. We shuffled the cards, we distributed them

(a) What is the probability that A has Miss Scarlett in his game?

(b) What is the probability that Miss Scarlett is the murder knowing that A has not Miss Scarlett in his game?

Expert Solution

1 )

a)

The probability of guessing the murder correctly before being given any information (beyond the rules of the game) will be 1/(9*6*6) = 1/324

because we have 3 piles: Pile 1 with 9 cards, pile 2 and pile 3 with 6 cards for each and they are all different.

b)

2)

a)

b)

orchestra answered 2 years ago

Given 8 cards: A, B, C, D, E, F, G, H How many ways can all...

Given 8 cards: A, B, C, D, E, F, G, H How many ways can all the cards be arranged if you select with replacement? How many ways can four cards be arranged if you select with replacement? How many permutations are possible if you select 5 cards without replacement? How many combinations are possible if you select 6 cards without replacement? If the B and C cards are made into A cards, and the E, F, and G cards...

Consider the cross: A/a; b/b; C/c; D/d; E/e x A/a; B/b; c/c; D/d; e/e a) what...

Consider the cross: A/a; b/b; C/c; D/d; E/e x A/a; B/b; c/c; D/d; e/e a) what proportion of the progeny will phenotypically resemble the first parent? b) what proportion of the progeny will genotypically resemble neither parent?

1. a. How many permutations are there of the letters {A,B,C,D,E,F}? Of there, how many are...

1. a. How many permutations are there of the letters {A,B,C,D,E,F}? Of there, how many are even? b. Express the permutation BAFEDC in P6 in cycle notation and determine whether it is even or odd. c. Determine the composition BAFEDC*BCAFDE in P6. Is the composition even or odd? d. What is the members of P6 whose cycle notation (1345)(26)?

If there are 7 total notes C, D, E, F, G, A, and B and if...

If there are 7 total notes C, D, E, F, G, A, and B and if a five-note melody is selected at random (so that all melodies counted in part (a) are equally likely to be chosen), what is the probability that the melody will include exactly two “A” notes, but no other repeated notes? (A few allowable examples: AACEG, ACAEG, DFACA, EAABC, etc.)

In how many ways can 7 people { A, B, C, D, E, F, G }...

In how many ways can 7 people { A, B, C, D, E, F, G } be seated at a round table if (a) A and B must not sit next to each other; (b) C, D, and E must sit together (i.e., no other person can sit between any of these three)? (c) A and B must sit together, but neither can be seated next to C or D. Consider each of these separately. For (c) you may NOT...

Seven people (A,B,C,D,E, F, and G) are seated in a row. Suppose A,B, and C are...

Seven people (A,B,C,D,E, F, and G) are seated in a row. Suppose A,B, and C are freshmen, D and E are sophomores and F and G are juniors. How many arrangements are possible if: (a) D and F must sit together? (b) A and C must not sit together? (c) All freshmen must sit together? (d) All freshmen must sit together, all sophomores must sit together, and all juniors must sit together? (e) Exactly two people sit between A and...

Assume that: float a, b, c, d, f; and variables b, c, d, f are initialized....

Assume that: float a, b, c, d, f; and variables b, c, d, f are initialized. Write a line of c++ code that calculates the formula below and stores the result to the variable a:

4 -letter words'' are formed using the letters A, B, C, D, E, F, G. How...

4 -letter words'' are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. Your answer is : (b) No letter can be repeated in a word. Your answer is : (c) Each word must begin with the letter A. Your answer is : (d) The letter C must be at the end. Your answer is : (e) The second letter must...

In how many ways can 9 people { A, B, C, D, E, F, G, H,...

In how many ways can 9 people { A, B, C, D, E, F, G, H, I } be seated at a round table if (A) A and B must not sit next to each other; (B) C, D, and E must sit together? (C) A and B must sit together, but neither can be seated next to C, D, or E. Consider each of these separately. For (C) you may NOT simply list all possibilities, but must use the...

(Circular Permutations) In how many ways can 7 people { A, B, C, D, E, F,...

(Circular Permutations) In how many ways can 7 people { A, B, C, D, E, F, G } be seated at a round table if (a) A and B must not sit next to each other; (b) C, D, and E must sit together (i.e., no other person can sit between any of these three)? (c) A and B must sit together, but neither can be seated next to C or D. Consider each of these separately. Hint: Conceptually, think...