Question

A dice is thrown once . list the
sample space (write all the possible
outcomes )
find the probabily of getting
1 .an add number
2. an even number
3. a prime number
4. a composite number 5 .a number that is neitheir prime nor composite
6. a factor of 6
7. proper factor of 6
8. a number <5
​

Answer 1

Answer:

P(A) = 1/2

P(B) = 1/2

P(C) = 1/2

P(D) = 1/3

P(E) = 1/6

P(F) = 2/3

P(G) = 1/3

P(H) = 2/3

Step-by-step explanation:

A dice is thrown

S is the sample space

∴S = { 1 , 2 , 3 , 4 , 5 , 6 }

∴ n(S) = 6

Let A be the event of getting an odd number

∴A = { 1 , 3 , 5 }

∴ n(A) = 3

∴ P(A) = n(A)/n(S) = 3/6 = 1/2

Let B be the event of getting an even number

∴ B = { 2 , 4 , 6 }

∴ n(B) = 3

∴ P(B) = n(B)/n(S) = 3/6 = 1/2

Let C be the event of getting a prime number

∴ C = { 2 , 3 , 5 }

∴ n(C) = 3

∴ P(C) = n(C)/n(S) = 3/6 = 1/2

Let D be the event of getting a composite number

∴ D = { 4 , 6 }

∴ n(D) = 2

∴ P(D) = n(D)/n(S) = 2/6 = 1/3

Let E be the event of getting a number that is neither prime nor composite

∴ E = { 1 }

∴ n(E) = 1

∴ P(E) = n(E)/n(S) = 1/6

Let F be the event of getting a number which is a factor of 6

∴ F = { 1 , 2 , 3 , 6 }

∴ n(F) = 4

∴ P(F) = n(F)/n(S) = 4/6 = 2/3

Let G be the event of getting a number which is a proper factor of 6

∴ G = { 2 , 3 }

∴ n(G) = 2

∴ P(G) = n(G)/n(S) = 2/6 = 1/3

Let H be the event of getting a number <5

H = { 1 , 2 , 3 , 4 }

∴ n(H) = 4

∴ P(H) = n(H)/n(S) = 4/6 = 2/3