Sino
nat
ahe
thrown together
Two
different dise
have (1) even sum (2) even product.
find probability that the numbers albtain
Answers
Answered by
8
Answer:
When two different dice are thrown together, the sample space is given by
S=
⎩
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎧
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
::
::
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
⎭
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎫
∴n(S)=36
A≡ event that sum of nos is even.
A=
⎩
⎪
⎪
⎨
⎪
⎪
⎧
(1,1)(1,3)(1,5)(2,2)(2,4)(2,6)
(3,1)(3,3)(3,5)(4,2)(4,4)(4,6)
(5,1)(5,3)(5,5)(6,2)(6,4)(6,6)
⎭
⎪
⎪
⎬
⎪
⎪
⎫
∴n(A)=18
P(A)=
n(S)
n(A)
=
36
18
=
2
1
B= event that the product is even.
B≡
⎩
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎧
(1,2)(1,4)(1,6)(2,1)(2,2)(2,3)
(2,4)(2,5)(2,6)(3,2)(3,4)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,2)
(5,4)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
⎭
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎫
∴n(B)=27
P(B)=
n(S)
n(B)
=
36
27
=
4
3
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