Probability, Random Variables, and Probability Distributions

10/324

25/324

50/648

100/1296

0.9449

0.56751

0.853

0.02

$\sqrt{2} \times 0.50$

12.50

25

50

Decrease in sample size

Increase in power of test

Increase in Type II errors

Decrease in effect size detected

Incorrect answers where the calculations include combining probabilities from different surveys.

Incorrect answers where computing only the number of successful responses for each event response.

Incorrect answers where yes trials occur across the whole survey.

Correct answers where the sum of five multiple choices with permutations based on the number of ways which the fifth question can be selected and success hats with multiple by the probability for success raised the third power failures the rest tings wer ncorrect answers where yes trials are summed incorrect answers where the calculations include combining probabilities from different surveys incorrect answer computing only the number of successful responses for each event restponse that does not consider the overall number possibilities.

1-\left(\left(\frac{1}{5}\right)^{20}\right)

$\binom{20}{17}\left(\frac{1}{5}\right)^{17}\left(\frac{4}{5}\right)^{3}$

$\sum_{k=17}^{20}\left(\binom{20}{k}\left(\frac{1}{5}\right)^{k}\left(\frac{4}{5}\right)^{20-k}\right)$

1-\left(\left(\frac{4}{5}\right)^{20}\right)

$10(0.8)^9(0.2)$

$0.8^2(0.2)^8 \binom{10}{2}$

$0.8^{10} + (0.20)^{10}$

$P(X=0) + P(X=1) + P(X=2)$

At least 29 games

Twenty games

Ten or more games

Forty games

0.4

0.5

0.2

0.8

$\left(\frac{1}{2}\right)^{20}$

$\binom{20}{15} (0.6)^{15} (0.4)^5$

$\binom{20}{5} (0.6)^5 (0.4)^{15}$

$\binom{20}{15} (0.5)^{15} (0.5)^5$