Simulating Multi-step Experiments

Warmup

Activity #1

Probability Simulation.

Simulation of flipping up to 10 coins, in which each coin is not necessarily “fair” (i.e. has 50/50% chance of landing Head/Tails).

• Use sliders to select the number of coins and the probability that each will land Heads (H). ​
• Use buttons to simulate a single flip, automate the whole flipping’ process, reset all coins to be fair, or restart to 0 trials. Beware that after several hundred trials, the app may start to drag.

Activity #2

`Probability Simulation.`

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.

• In each trial, spin the spinner 10 times, and then record the number of 1’s that appeared in the row.
• The applet reports if the Alpine Zoom will make money or not in the last column.
• Click to get the spin button back to start the next simulation.

(1.) Based on your simulations above, estimate the probability that Alpine Zoom will make money.

(2.) Describe a chance experiment that you could use to simulate whether it will snow on the first day of break.

Activity #3

`Practice Probability Simulation.`

• Read the story below and complete the exercise.

Priya’s cat is pregnant with a litter of 5 kittens. Each kitten has a 30% chance of being chocolate brown. Priya wants to know the probability that at least two of the kittens will be chocolate brown.

To simulate this, Priya put 3 white cubes and 7 green cubes in a bag. For each trial, Priya pulled out and returned a cube 5 times. Priya conducted 12 trials.

Here is a table with the results.

(2.) Based on this simulation, estimate the probability that exactly two kittens will be chocolate brown.

(3.) Write and answer another question Priya could answer using this simulation.

(4.) How could Priya increase the accuracy of the simulation?

Challenge #1

Match each situation to a simulation.

Challenge #2

Quiz Time