Task : carnival games

the community carnival has a ball toss game with three rectangular boards as targets. all three rectangles have the same dimensions. the holes in the middle of the boards have different shapes and dimensions, as shown in the image below. (note: the images are not drawn to scale.)

what is the probability of hitting each target if it is assumed that a player’s throw will always hit the board? hint: the probability of hitting each target is the area of the target hole divided by the total area of the target. take the value of π to be 3.14.

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to win the grand prize, a player must toss the ball into the hole in one try for each of the three targets. find the probability of winning the grand prize. (hint: the probability of a set of events occurring is equal to the product of the probabilities of each individual event occurring.)

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rewrite the expression you found in part b into the form .

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if the value of x is 2, find the probability of a player winning the grand prize.

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a player who hits only the first two targets gets a runner-up prize. write an expression that represents this scenario. (hint: to find the probability of hitting the first two targets, divide the expression you derived in part b by the expression representing the probability of hitting the third target.)

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rewrite the expression you obtained in part e in the form.

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