Question

question 20
a football coach is trying to decide: when a team is ahead late in the game, which strategy is better?

• play the

egular\ defense.

• play a \prevent\ defense that guards against long gains but makes short gains easier.

the coach reviews the outcomes of 100 games.

compare the probability of winning when playing regular defense with the probability of winning when playing prevent defense. draw a conclusion based on your results.
a. $p(\text{win} | \text{regular}) = 0.84$
$p(\text{win} | \text{prevent}) = 0.70$
conclusion: you are more likely to win by playing prevent defense.
b. $p(\text{win} | \text{regular}) = 0.35$
$p(\text{win} | \text{prevent}) = 0.65$
conclusion: you are more likely to win by playing prevent defense.
c. $p(\text{win} | \text{regular}) = 0.84$
$p(\text{win} | \text{prevent}) = 0.70$
conclusion: you are more likely to win by playing regular defense.
d. $p(\text{win} | \text{regular}) = 0.35$
$p(\text{win} | \text{prevent}) = 0.65$
conclusion: you are more likely to win by playing regular defense.

question 21
find the value of $7!$.
a. 823,543
b. 5040
c. 42
d. 49

question 22
you have 6 different trophies to arrange on the top shelf of a bookcase. how many ways are there to arrange the trophies?
a. 120
b. 36
c. 720
d. 5040

Explanation:

Question 20

Step1: Calculate P(win|regular)

$P(\text{win}|\text{regular}) = \frac{42}{50} = 0.84$

Step2: Calculate P(win|prevent)

$P(\text{win}|\text{prevent}) = \frac{35}{50} = 0.70$

Step3: Compare probabilities

$0.84 > 0.70$, so regular defense has higher win probability.

Step1: Define factorial operation

$n! = n\times(n-1)\times...\times1$

Step2: Compute 7!

$7! = 7\times6\times5\times4\times3\times2\times1 = 5040$

Step1: Recognize permutation of 6 items

Number of arrangements = $6!$

Step2: Calculate 6!

$6! = 6\times5\times4\times3\times2\times1 = 720$

Answer:

C. P (win | regular) = 0.84
P (win | prevent) = 0.70
Conclusion: You are more likely to win by playing regular defense.

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Question 21