need both question\'s all parts 2. One jar has 6 ping pong balls, taking one bal

Question

need both question's all parts

2. One jar has 6 ping pong balls, taking one ball form the first jar, and then taking a ball from the second jar labeled 1, 2,3,4, 5, 6. A second jar has 4 ping pong balls, labeled 1, 2.3, 4. An experiment consists of a. [12.5 pts) Write-out the listing all the out atcome Sample Space,S (using sct braces notation). What is aS)? Use ordered pair notation when in S: “ ( e,") “ (7.5 pts]: Write-out the event Ei that the number on the first ping pons ball is greater than the number on the second one using set braces notation). What is n(E)2 Use ordered pair notation when listing all the outcomes. c. [2.5 pts]: Write-out the event E, that the sum of the numbers on the What is n(E)? Use ordered pair notation when listing all the outcomes. two ping pong balls is 7 (using set braces notation). d. [1.5 pts]: Write-out the event Es tha What is n(E? Use ordered pair notation when listing all the outcomes. t the sum of the numbers on the two ping pong balls is 1 (using set braces notation). 3. A single fair die is rolled. Find the probabilities of each of these events. a. [3 pts]: Getting an even number. b. [3 pts]: Getting a number bigger than 4. c. [3 pts]: Getting a 2 or 4.

Explanation / Answer

Jar 1 : Six Balls with numbers 1,2,3,4,5,6

Jar 2 : four balls with numbers 1,2,3,4

a. Sample Sapce S :

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

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

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

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

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

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

n(S) : Number elements in the sample sapce = 24

b. Event E1 : Number on the first ball is greater than the number on the second ball

From the above sample space : S get all the outcomes where first number greater than second number they are

(2,1)

(3,1) (3,2)

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

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

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

n(E1) : Number of elements in the above event space = 14

c. Event E2 : Sum of the numbers on the two pinpong balls is 7

From the sample space in a. find all the elements whose sum is 7:

They are

(3,4)

(4,3)

(5,2)

(6,1)

n(E2) : Number of elements in the above event space = 4

d.  Event E3 : Sum of the numbers on the two pinpong balls is 1

From the sample space in a. Can not find any element who sum of the numbers on the tow ping pong balls =1

Hence

Event E3 is null

n(E2) : Number of elements in the above event space = 0

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