Question

Can someone help me in number 1, 2 and 3?

Thank you

1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements. (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let z be the outcome on the green die and y be the outcome on the red die. Describe the sample space S by using the rule method 2. If S-(x | 0 < x < 12). M-(x | 2 < x < 6), and N = {x | 4 < x < 12), find (a) MUN (b) Mn N (c) (Sn Ny (d) M'nN 3. A pair of fair dice are tossed. Find the probability of getting (a) a total of 4. (b) at most a total of 4

Answer 1

1.A.

Sample Space = { H, TH, TTH, TTTH, TTTT)

B.

Rule :

{(x,y)}:x,y∈{1,2,3,4,5,}

Sample Space:

1,1)	(1,2)	(1,3)	(1,4)	(1,5)
(2,1)	(2,2)	(2,3)	(2,4)	(2,5)
(3,1)	(3,2)	(3,3)	(3,4)	(3,5)
(4,1)	(4,2)	(4,3)	(4,4)	(4,5)
(5,1)	(5,2)	(5,3)	(5,4)	(5,5)

2.

S = {1,2,3,4,5,6,7,8,9,10,11,}

M = {3,4,5}

N = {5,6,7,8,9,10,11,}

Thus,

a. M U N = {3,4,5,6,7,8,9,10,11}

b. M ∩ N = {5}

c. (S∩N)' = {1,2,3,4}

d. M' ∩ N' = (M U N)' = S - (M U N) = {1,2}

3.

Sample Space =  

(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

a. Total events, S = 36

Events having sum of 4, A = {(1,3), (3,1), (2,2)}

Probability(A) = No. of events in A/No. of events in S = 3/36 = 1/12

b.

Total events, S = 36

Events having sum at most 4, B= {(1,3), (3,1), (2,2), (1,1), (1,2), (2,1)}

Probability(B) = No. of events in B/No. of events in S = 6/36 = 1/6