ACT 1 Geo: Find geometric probability

$Q_{1}:$ The figure shown is a rectangle. If a point is chosen at random. What is the probability that it will fall in the shaded region?

$Q_{2}:$ In the spinner modeled below, Sector $1$ has twice the area of Sector $3$. If the arrow is spun once, what is the probability that the arrow will land in Sector $1$?

$Q_{3}:$ The figure below shows two concentric circles, each divided into eight congruent segments. The area of the large circle is exactly twice that of the smaller circle. If a point is selected at random from the large circular region, what is the probability that the point will lie in a shaded portion of that circle?

$Q_{4}:$ In the figure shown is a rectangle, if a point chosen at random, what is the probability that it will fall in the shaded region?

$Q_{5}:$ What is the probability that a randomly selected point will fall in the shaded region?

$Q_{6}:$ A bus arrives at a particular bus stop every $20$ minutes. if you are to show up at the bus stop at a random time, what is the probability that you would be waiting for $4$ minutes or less?

$Q_{7}:$ A bus arrives at a particular bus stop every $20$ minutes. if you are to show up at the bus stop at a random time, what is the probability that you would be waiting for somewhere from $8-15$ minute?

$Q_{8}:$ A bus arrives at a particular bus stop every $20$ minutes. if you are to show up at the bus stop at a random time, what is the probability that you would be waiting for $18$ minute or more?

$Q_{9}:$ Ahmad makes $25\%$ of the three-point shots he attempts. For a warm up, Ahmad likes to shoot three-point shots until he successfully makes one. Let $K$ be the number of shots it takes Ahmad to successfully make his first three-point shot. Assume that the results of each shot are independent. Find the probability that Ahmad's first successful shot occurs on his $3^{rd}$ attept?

$Q_{10}:$ Find the probability that a randomly chosen point in the figure lies in the shaded region.

$Q_{11}:$ Find the probability that a randomly chosen point in the figure lies in the shaded region.

$Q_{12}:$ Find the probability that a randomly chosen point in the circle lies in the inscribed octagon.

$Q_{13}:$ A selection is to be made between points $G$ and $F$ as seen below. Find the probability that selection falls in $GH$

$Q_{14}:$ A selection is to be made between points $G$ and $F$ as seen below. Find the probability that selection falls in $FJ$

$Q_{15}:$ A selection is to be made between points $G$ and $F$ as seen below. Find the probability that selection falls in $HF$

$Q_{16}:$ A selection is to be made between points $G$ and $F$ as seen below. Find the probability that selection falls in $GH$ OR $HF$

$Q_{17}:$ The Stagecoach bus runs every $15$ minutes at Frimley. It takes Ahmad $10$ minutes to get to school from the bus stop. If Ahmad arrives at the bus station at half-past seven and is expected to get to school at quarter to eight. What is the probability that he reaches his school on time?

$Q_{18}:$ A circular path has been divided into $3$ regions, arcs $D, E$ and $F$. Find the probability a seedling growing a circular path is found in arc $E$ if the arc length of $D$ is $5$cm, the arc length of $F$ is $12$cm and the radius of the circular path is $7$cm. Take $\pi =\frac{22}{7}$.

$Q_{19}:$ We have rectangular lawn with a length $15$cm and width $30$cm. A equilateral triangle sandy court has been created inside the lawn with height $8$cm and side $6$cm . If a golfer hits a golf into the lawn, what is the probability that the golf hits the sandy court?

$Q_{20}:$ The figure below is a target. If its longest and shortest radii are 56cm and 7cm respectively. Find the probability of an arrow not hitting the bull's eye (the red spot). Take $\pi =\frac{22}{7}$

$Q_{21}:$ In a dart game, the target board is a circle with a radius of $6$ inches. If a player randomly throws a dart, what is the probability that the dart will hit a specific smaller circle at the center with a radius of $2$ inches?

$Q_{22}:$ You have a rectangular garden that measures $10$ feet in length and $8$ feet in width. If a randomly dropped seed lands anywhere in the garden, what is the probability that it will land within $2$ feet of the shorter side of the garden?

$Q_{23}:$ A square-shaped cookie sheet with a side length of $12$ inches has a circular pizza placed on it with a radius of $6$ inches. If you randomly place a fork on the cookie sheet, what is the probability that it will land on the pizza and not on the empty cookie sheet?

$Q_{24}:$ In a game of darts, the dartboard consists of a circular bullseye at the center with a radius of $2$ inches, and a larger outer ring with a radius of $6$ inches. If a player throws a dart randomly, what is the probability that it lands within the bullseye?

$Q_{25}:$ You are playing a game where you throw a beanbag onto a square target board with side lengths of $4$ feet. The target board is divided into four equal squares. What is the probability that the beanbag lands in one of the corner squares?