Answer:
Layers P, Q, R, and S are the same as layers IV, V, VI and VII.
Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.
<h3>What is the binomial probability distribution?</h3>
It is the probability of <u>exactly x successes on n repeated trials, with p probability </u>of a success on each trial.
The expected number of trials until q successes is:

In this problem, the parameters are given as follows:
q = 50, p = 0.32.
Hence:

More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer: 1537.
Step-by-step explanation:
Formula for sample size :-

Given :
Margin of error : E= 100
Critical value of 95% confidence : 
Now, the required sample size will be :-

Hence, the minimum sample size required = 1537.
Answer:
88 divided by 8 is 11.
Step-by-step explanation:
You can't use the distributive property for this problem because there is no distributing to be done, but the answer is 11.