Question

Can someone help me with this problem AS SOON AS POSSIBLE!!!!!

I don’t know how to do this one after I tried multiple times !!!

Answer 1

the total amount of students in the diagram is 69, so that'd be our sample space.

P(Rhythm | Smooth)

well, from the diagram the ones who did both is 9 + 6, so our favorable outcomes is 9 + 6 = 15.

`\cfrac{\stackrel{\textit{favorable outcomes}}{15}}{\underset{\textit{sample space}}{69}}\implies \cfrac{5}{23} ~~ \approx ~~ \text{\LARGE 21.7\%}`

P(Rhythm | Standard)

the overlapping on both those is 6 + 10 = 16

`\cfrac{\stackrel{\textit{favorable outcomes}}{16}}{\underset{\textit{sample space}}{69}} ~~ \approx ~~ \text{\LARGE 23.1\%}`

P(Standard | Rhythm)

pretty much the same probability as before, just worded differently.

P(Rhythm | Smooth OR Standard)

well, the ones overlapping Rhythm with Smooth and Standard are 9 + 6 + 10 = 25, so 25 out of 69.

`\cfrac{\stackrel{\textit{favorable outcomes}}{25}}{\underset{\textit{sample space}}{69}} ~~ \approx ~~ \text{\LARGE 36.2\%}`