Part I

Area of region 1/Total area = probability of a dart landing in region 1.

Because probability = desired outcome/all possible outcomes.

Area of region 1= ¹r²=¹20²=400¹cm².

Total area =¹r²=¹40²=1600¹ cm².

Area of region 1/Total area =400¹ cm²/1600¹ cm²=1/4=.25

Since Region 1 is 400¹ or 1/4 of the total area of 1600¹ cm², region 2 must be 3/4 of the area or 1200¹ cm². So, the probability of a dart, thrown at random, landing in region 2 is .75.

Out of 50 throws 1/4 will land in region 1. 50*.25=12.5

3/4 of the throws will land in region 2. 50*.75=37.5

Thus we have 12.5 throws at 10 points per throw. 12.5 throws *10=125 points

Thus we have 37.5 throws at 5 points per throw. 12.5 throws *10 =187.5 points.

187.5 points +125 points =312.5 points

Or after four throws the score should be 10+5+5+5=25. So after 100 throws the score should be 25*25=625, so after 50 throws the score should be 312.5

You can't have a score of 312.5, scores can only be whole numbers, what should we do about the ".5"?