Students will build Grade 7 mastery of simulating compound events using models, equations, and test-style reasoning.
To simulate the probability of guessing a true/false question correctly \(3\) times in a row, which tool best models this compound event?
A spinner has \(6\) equal sections. To simulate rolling a standard die once, how many trials are needed if we spin once per trial?
Which simulation tool best models the probability of selecting a red marble or a blue marble from a bag with equal numbers of red and blue marbles?
A bag contains \(3\) red marbles, \(2\) blue marbles, and \(5\) green marbles. To simulate drawing one marble, which probability does rolling a standard die best represent?
To simulate drawing a card from a standard deck and finding whether it is a heart (probability \(\frac{1}{4}\)), which spinner design is best?
A spinner with \(4\) equal sections (Red, Blue, Green, Yellow) is spun twice to simulate a compound event. If "success" is defined as "the first spin is Red and the second spin is Blue," how many outcomes in the sample space represent a success?
Two fair dice are rolled as a simulation of a compound event. If "success" is rolling a sum of \(7\), which of the following correctly identifies all successful outcomes?
A coin is flipped \(100\) times. Heads appears \(48\) times. Based on this simulation, which is the estimated probability of flipping heads?
Each true/false question has \(2\) equally likely outcomes (like a coin). The compound event is three consecutive guesses, so three flips simulate this.
A spinner with \(6\) equal sections directly models one roll of a die (one outcome per spin).
Two equally likely outcomes (red or blue, heads or tails) match perfectly.
There are \(5\) green marbles out of \(10\) total, giving probability \(\frac{5}{10} = \frac{1}{2}\). Rolling \(1\)--\(3\) on a die simulates this (or rolling odd/even).
Probability \(\frac{1}{4}\) means \(1\) favorable outcome out of \(4\) equally likely ones.
The sample space has \(4 \times 4 = 16\) equally likely outcomes. Only one outcome satisfies the condition: "first spin Red, second spin Blue."
Each standard die shows \(1\)--\(6\), so \((1,7)\) is impossible. To get a sum of \(7\), identify all pairs \((a, b)\) where \(a + b = 7\) and \(1 \leq a, b \leq 6\). These are the six outcomes listed. The probability is thus \(\frac{6}{36} = \frac{1}{6}\).
Relative frequency from the simulation is \(\frac{48}{100} = 0.48\), which estimates the probability.
