Lesson 7 Slacker’s Simulation Solidify Understanding

Ready

1.

Are the two matrices equal? Explain your answer.

$A = [\begin{matrix} - 3 & 2 & 7 \\ 4 & 36 & 3 \end{matrix}]$

$B = [\begin{matrix} \frac{- 12}{4} & \sqrt{4} & \frac{- 21}{- 3} \\ \frac{64^{\frac{1}{2}}}{2} & 6^{2} & \sqrt[3]{27} \end{matrix}]$

2.

Are the two matrices equal? Explain your answer.

$C = [\begin{matrix} - 9 & 1 & 13 \end{matrix}]$

$D = [\begin{matrix} - 9 \\ 1 \\ 13 \end{matrix}]$

3.

Can matrix $A$ and matrix $C$ be added? Explain your answer.

4.

Can matrix $A$ and matrix $D$ be multiplied? If your answer is yes, describe the product of $A D$ . If your answer is no, explain why not.

5.

Is matrix addition commutative? Explain your answer.

6.

Is matrix multiplication commutative? Explain your answer.

Set

In 1963, NBC started to host a game called Let’s Make a Deal! Contestants were given three doors to choose from. Behind one door was a prize. After selecting one door, the contestant was shown what was behind one of the doors they did not select. The contestant is then asked if they would like to stay with the door they first selected or switch to the remaining one.

7.

Which strategy do you think would result in the best chance of selecting the winning door? Should the contestant switch doors or stay with the first one they chose?

Go to the following website: openup.org/m3Eb7f

8.

Play the game $20$ times using the stay method and $20$ times using the switch method. Record your wins and losses in the table.

	Stay	Switch	Total
Win
Lose
Total

9.

Based on the simulation, $P (winning | stay) =$

10.

Based on the simulation, $P (winning | switch) =$

11.

Simulate $100$ games for each strategy. What is the probability of winning using each method?

Go

	Stay	Switch	Total
Win	$6$	$12$	$18$
Lose	$14$	$8$	$22$
Total	$20$	$20$	$40$

12.

Create a Venn diagram and a tree diagram using the data shown in the table.

13.

$P (winning) =$

14.

$P (winning \cap staying) =$

15.

$P (winning \cup staying) =$

16.

$P (losing | staying) =$

17.

$P (winning or losing) =$

18.

Are the events winning and staying independent of each other? Justify your answer using probabilities.