Question

Find the probability of winning a new tvFind the odds against the team winning its next match

Answer 1

a)

`(2)/(7)`

b)

`(12)/(11)`Step-by-step explanation

The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring, the probability is givenby:

`P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}`

so

Step 1

we can find the odds in favor by using the expression:

`Odds\text{ in favor=}(P(A))/(1-P(A))`

so

let

`\begin{gathered} P(A)=unknown \\ odds\text{ in favor=}(2)/(5) \end{gathered}`

now, replace and solve for P(A)

`\begin{gathered} Odds\text{ in favor=}(P(A))/(1-P(A)) \\ (2)/(5)=(P(A))/(1-P(A)) \\ cross\text{ multiply } \\ 2(1-P(A))=5*P(A) \\ 2-2P(A)=5P(A) \\ add\text{ 2P\lparen A\rparen in both sides} \\ 2-2P(A)+2P(A)=5P(A)+2P(A) \\ 2=7P(A) \\ divide\text{ both sides by 7} \\ (2)/(7)=(7P(A))/(7) \\ (2)/(7)=P(A) \end{gathered}`

therefore, the probabilyt of winning a new TV is

`(2)/(7)`

Step 2

now, to find the odds against we need to use the formula:

`odds\text{ agains=}(1-P(A))/(P(A))`

so

let

`P(B)=(11)/(23)`

now, replace in the formula and calculate

`\begin{gathered} odds\text{ against=}(1-P(A))/(P(A)) \\ odds\text{ against=}(1-(11)/(23))/((11)/(23)) \\ odds\text{ against=}((12)/(23))/((11)/(23))=(12*23)/(11*23)=(12)/(11) \\ odds\text{ against=}(12)/(11) \end{gathered}`

therefore, the odds against are

`(12)/(11)`

I hope this helps you