(a) The probability that an athlete will not win any of three races is 1/4.If the athlete runs in all the races, what is the probability that the athlete wi...

9(a)(i)

p = 14 $\frac{\mathrm{<br>}}{}$,

p = 1 - 14 $\frac{\mathrm{<br>}}{}$

p = 34 $\frac{\mathrm{<br>}}{}$

= 364 $\frac{\mathrm{<br>}}{}$

= 0.04687 ≈ 0.05

(ii) p(winning all) = 34 $\frac{\mathrm{<br>}}{}$ * 34 $\frac{\mathrm{<br>}}{}$ * 34 $\frac{\mathrm{<br>}}{}$

= 2764 $\frac{\mathrm{<br>}}{}$ = 0.422

(iii) p(winning two)

= (34 $\frac{3}{4}$ * 34 $\frac{3}{4}$ * 14 $\frac{1}{4}$) + (34 $\frac{3}{4}$ * 14 $\frac{1}{4}$ * 34 $\frac{3}{4}$) + (14 $\frac{1}{4}$ * 34 $\frac{3}{4}$ * 34 $\frac{3}{4}$)

= 964 $\frac{9}{64}$ + 964 $\frac{9}{64}$ + 964 $\frac{9}{64}$

= 2764 $\frac{27}{64}$ = 0.4218

= 0.42

(b) Volume of a cone = 1/3πr2 ${}^{\mathrm{<br>}}$h

 1200 = 13 $\frac{\mathrm{<br>}}{}$ * 227
 * r2 ${}^{\mathrm{<br>}}$ * 24

r2 ${}^2$ = 1200∗3∗722∗24 $\frac{\mathrm{<br>}}{}$

r2 ${}^2$ = 25200528 $\frac{\mathrm{<br>}}{}$

r2 ${}^2$ = 47.727

r = 4–√7.727

r =  6.9085cm

Volume of a cone with same radius and height 84cm:

v =  13 $\frac{\mathrm{<br>}}{}$ *  227 $\frac{\mathrm{<br>}}{}$ * (6.9085)2 ${}^{\mathrm{<br>}}$ * 84

= 13 $\frac{\mathrm{<br>}}{}$ *  227
 * 47.727 * 84

volume = 4200cm3