Hi all I am having problems withthis: When two fair dice are rolled, 36 equallyl

Question

Hi all I am having problems withthis:

When two fair dice are rolled, 36 equallylikely outcomes are possible as shown below.
(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)

Let X = Maximum of the numbersshown on the dice. Find the probability distribution of X. Give theprobabilities rounded to three decimal places.

a) Find the mean and standard deviation of the random variableX
b) Let A be the event that X is an even number. Find P(A)
c) Let B be the event that X is 2. Find P(B)

Please Show All Work, Thank You, Will Give ALIFESAVER

Explanation / Answer

x=2, P(2)=1/36 x=3, P(3)= 2/36 because (1,2) or (2,1) x=4, P(4)= 3/36 x=5, P(5)=4/36 x=6, P(6)=5/36 x=7, P(7)=6/36 x=8, P(8)=5/36 x=9,P(9)=4/36 x=10, P(10)=3/36 x=11, P(11)=2/36 X=12, P(12)=1/36 mean=2(1/36)+3(2/36)+4(3/36)+.......+11(2/36)+12(1/36)=252/36=7 2=(2-7)2(1/36)+(3-7)2(2/36)+...+(11-7)2(2/36)+(12-7)2(1/36)=[25+32+27+16+5+0+5+16+27+32+25]/36 =(210/36)= 2.145 b)P(even)=P(2 or 4 or 6 or or8 or 10 or12)=[1+3+5+5+3+1]/36=18/36=.5 c) P(B)=1/36

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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