probability.?

Question

(a)Two fair tetrahectral dice are rolled. if each is numbered 1-4 draw two way table to show all possible outcomes

(b)What is the probability that both dice show the same Number..

(c)What is the probability that the number on one dice is double the number on other

(d) What is the probability that the sum of both numbers are prime..

Answer 1

qa
(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)

qb
(1,1) (2,2) (3,3) (4,4)
n(onaji suuji) = 4

P = 4/16 = 1/4

qc
(1,2)
(2,1) (2,4)
(4,2)
n(one double another) = 4

P = 4/16 = 1/4

qd
(1,1) (1,2) (1,4)
(2,1) (2,3)
(3,2) (3,4)
(4,1) (4,3)
n(prime sum) = 9

P = 9/16

Answer 2

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

4/16 = 1/4

2/16 = 1/8

8/16 = 1/2

Answer 3

Two dice each numbered from 1 to 4.
Possible outcomes
a)
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
Each of the outcome has a probability of 1/16 if the dice are fair.

b) p(same number)=4/16
(1,1)(2,2)(3,3)(4,4)

c)(1,2),(2,1),(2,4),(4,2) = 4/16

d)(1,2)=3
(1,4)=5
(2,1)=3
(2,3)=5
(3,2)=5
(3,4)=7
(4,1)=5
(4,3)=7
8/16=1/2

Answer 4

Both of the above answers are right except for part (d).

They forgot to add in the roll of 1,1 = 2 which is also a prime number. 9/16 is the right answer.

Answer 5

Question a:
There are 16 possiblities (4 x 4 = 16):

(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)

Question b:
(1,1),(2,2),(3,3),(4,4)
4/16 = 1/4

Question c:
(1,2),(2,1),(2,4),(4,2)
4/16 = 1/4

Question d:
(1,1)=2
(1,2)=3
(1,4)=5
(2,1)=3
(2,3)=5
(3,2)=5
(3,4)=7
(4,1)=5
(4,3)=7
so, = 9/16