Question

There is a spinner with 5 equal sections. Red, Red, Blue, Green and Yellow.

1.If Jo spins a Blue and a Red (or a Red and a Blue) he wins. What is the PROBABILITY that Jo wins?

2. If Mara spins a Red and a Red or a Yellow first then a Red she wins. What is the PROBABILITY that Mara wins?

Answer 1

Answer :

We know Probability P ( E ) = $\frac{Numberofdesiredeventsn(\hspace{0.17em}E)}{Totalnumberofeventsn(S\hspace{0.17em})}$

1 ) If Jo spins a Blue and a Red (or a Red and a Blue) he wins

SO, Desired events { ( B , R ) And ( R , B ) }
Total events if Blue comes first : { ( B , R ) , ( B , G ) , ( B ,Y ) }

Total events if Red comes first : { ( R , R ) , ( R , B ) , ( R , G ) , ( R , Y ) }

SO, Winning probability of Jo if combination ( B , R ) came = $\frac{1}{3}$

Winning probability of Jo if combination ( R , B ) came = $\frac{1}{4}$

So, Winning probability of jo if a Blue and a Red or a Red and a Blue comes = $\frac{1}{3}$ + $\frac{1}{4}$ = $\frac{4+3}{12}=\frac{7}{12}$ ( Ans )

2 ) If Mara spins a Red and a Red or a Yellow first then a Red she wins.

SO, Desired events { ( R , R ) And ( Y , R ) }
Total events if Yellow comes first : { ( Y , R ) , ( Y , G ) , ( Y ,B ) }

Total events if Red comes first : { ( R , R ) , ( R , B ) , ( R , G ) , ( R , Y ) }

SO, Winning probability of Jo if combination ( Y , R ) came = $\frac{1}{3}$

Winning probability of Jo if combination ( R , R ) came = $\frac{1}{4}$

So, Winning probability of Mara , If she spins a Red and a Red or a Yellow first then a Red = $\frac{1}{3}$ + $\frac{1}{4}$ = $\frac{4+3}{12}=\frac{7}{12}$ ( Ans )