IM 7.8.7 Lesson: Simulating Multi-step Experiments
What do you notice? What do you wonder?
Alpine Zoom is a ski business. To make money over spring break, they need it to snow at least 4 out of the 10 days. The weather forecast says there is a chance it will snow each day during the break. Use the applet to simulate the weather for 10 days of break to see if Alpine Zoom will make money. Describe a chance experiment that you could use to simulate whether it will snow on the first day of break.
How could this chance experiment be used to determine whether Alpine Zoom will make money?
Based on your simulations, estimate the probability that Alpine Zoom will make money.
Kiran invents a game that uses a board with alternating black and white squares. A playing piece starts on a white square and must advance 4 squares to the other side of the board within 5 turns to win the game.
For each turn, the player draws a block from a bag containing 2 black blocks and 2 white blocks. If the block color matches the color of the next square on the board, the playing piece moves onto it. If it does not match, the playing piece stays on its current square.
Take turns playing the game until each person in your group has played the game twice.
Use the results from all the games your group played to estimate the probability of winning Kiran’s game.
Do you think your estimate of the probability of winning is a good estimate? How could it be improved?
How would each of these changes, on its own, affect the probability of winning the game?
Change the rules so that the playing piece must move 7 spaces within 8 moves.
Change the board so that all the spaces are black.
Change the blocks in the bag to 3 black blocks and 1 white block.
Match each situation to a simulation. In a small lake, 25% of the fish are female. You capture a fish, record whether it is male or female, and toss the fish back into the lake. If you repeat this process 5 times, what is the probability that at least 3 of the 5 fish are female?
Elena makes about 80% of her free throws. Based on her past successes with free throws, what is the probability that she will make exactly 4 out of 5 free throws in her next basketball game?
On a game show, a contestant must pick one of three doors. In the first round, the winning door has a vacation. In the second round, the winning door has a car. What is the probability of winning a vacation and a car?
Your choir is singing in 4 concerts. You and one of your classmates both learned the solo. Before each concert, there is an equal chance the choir director will select you or the other student to sing the solo. What is the probability that you will be selected to sing the solo in exactly 3 of the 4 concerts?