Question

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 r 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, lf S = {x | 0 < x < 12). Λι = {" I 2 < x <6), and N = {x | 4 <1<12), find (a) MUN (b) MnN (c) (Sn N) (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.

all questions please

Answer 1

Solution

Q1 Part (a)

Let S1 = {H, TH, TTH, TTTH, ……….. }, and

S2 = {TTTT, HTTTT, THTTTT, HTHTTTT, THHTTTT, …….}. Then,

S = S1∪ S2. Answer 1

Q1Part (b)

Sample space, S = {x, y | 1 ≤ x ≤ 5, 1 ≤ y ≤ 5, x,y ∈ N} Answer 2

Q2 Part (a)

M ∪ N = {x | 2 < x < 12} Answer 3

Q2 Part (b)

M ∩ N = {x | x = 5} Answer 4

Q2 Part (c)

(S ∩ N)’ = {x | 4 < x < 12}’

= {x | x ≤ 4, x ≥ 12} Answer 5

Q2 Part (d)

M’ ∩ N’ = {x | x ≤ 2, x ≥ 12} Answer 6

Q3 Part (a)

Sum = 4 => (1, 3), (2, 2), (3, 1) are the only possibilities. Since totally there (6 x 6) = 36 possibilities, the required probability = 3/36 = 1/12 Answer 7

Q3 Part (b)

Sum = at most 4 => Sum = 2 ,3 or 4 => (1, 1), (1, 2), (2, 1), (1, 3), (2, 2), (3, 1) are the only possibilities. Since totally there (6 x 6) = 36 possibilities, the required probability = 6/36

= 1/6 Answer 8

DONE