Find the odds for and the odds against the event rolling a fair die and getting a 2 comma a 4 comma a 5 comma or a 3.

The event of rolling a fair die and getting 2 or 4 or 5 or 3 has 4 possible outcomes. Either one can get 2 or 4 or 5 or 3

Number of possible ways of getting favorable outcome =4

Now remaining outcomes which are not included into event are getting 1 or 6. There are 2 outcomes.

Number of possible ways of getting unfavorable outcome =2

Odds for the event = Number of ways getting favorable outcome / Number of ways getting unfavorable outcome

Odds for given event = 4 /2 = 2/1

Odds against eventSo the odds for event of rolling a fair die and getting 2 or 4 or 5 or 3 is 2:1

Odds against event = Number of ways of getting unfavorable event / Number of ways of getting favorable event

= 2/4

=1/2

So the odds against event of rolling a fair die and getting 2 or 4 or 5 or 3 is 1:2

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)