Question

A fly lands at random at a point on the grid. Find the probability of the fly landing on the figure.



A. 9/35

B. 9/70

C. 18/70

D. 9/61

I chose A and got it incorrect .

Answer 1

Geometric probability here is \( \displaystyle \frac{\text{Area of figure (acceptable outcome)}}{\text{total area (all possible outcomes}} \)

The total area of the grid is pretty easy, just count the squares for base and height, then multply.

The figure, we would use A = 1/2 b * h of the triangle.

Answer 2

okay , i got 35 when i did A=1/2*b*h

Answer 3

i counted 10 blocks on the bottom and 7 on the side

Answer 4

1/2*b*h was for the triangle figure in the middle, sorry if i wasn't clear there.

The entire grid's area is just b*h, or 7*10 = 70. :)
For the triangle, we could count the number of squares along the base of the figure and then the height from that base to the highest tip on the triangle for the height. Then just plug into that A = 1/2 b*h formula. :)

Answer 5

okay :) i got 7 on the bottom for the triangle and 4 one the side then when i did A=1/2*b*h i got 14

Answer 6

hmm, we can't include that extra square beneath the upper vertex because nothing is there, at least in terms of the base's length. We'd only have 6 blocks under the triangle's actual base. The height would be 3 blocks here as well, just counting from the 'line containing the base' to the vertex, like in my previous drawing.

Answer 7

http://puu.sh/1BfYC Like this, if that's more clear

Answer 8

oh goodness i see my mistake i counted a block that wasn't even there , sorry :) so it would be 9 then for the area of the triangle?

Answer 9

Yes. :)
So, just take the quotient: Area of Triangle/ Area of Grid
A of Triangle = 9, A of grid = 70
so 9/70.

Answer 10

0.128..... which would be B? do i just test each answer choice?

Answer 11

well 9/70 was the option for B, so that should be correct. The other answers don't look like they'll be the same fraction since 9/70 is in simplest form and the next bump up is 2/2*9/70, or 18/140. :p

Answer 12

okay , thanks so much for the help! :)

Answer 13

You're welcome! :)