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Molodets [167]
2 years ago
13

Suppose an NBA basketball player shooting an uncontested 2-point shot will make the basket with probability 0.6. How- ever, if y

ou foul t he shooter, t he shot 'vill be missed, but t'vo free thro,vs will be a'varded. Each free thro'v is an independent Bernoulli trial 'vith success probability p. Based on the expected number of points the shooter 'vill score, for what values of p may it be desirable to foul the shooter?
Mathematics
1 answer:
Snezhnost [94]2 years ago
8 0

Answer:

0.06

Step-by-step explanation:

The computation of the value of p is shown below;

P in the case (2 points if not fouled) = 0.6

Now Expected points if not fouled is

= 0.6 × 2

= 1.2

Now Expected points from free throw is

0 × (1-p)^2 + 1 × 2p(1-p) + 2 × p^2 = 2p

As we can see that 2p would be lower tha  1.2 in order to make a foul on shooter that represent all values of p<0.06 would be considered to foul in the shooter

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Read 2 more answers
A substance with a half life is decaying exponentially. If there are initially 12grams of the substance and after 70 minutes the
dybincka [34]

Answer:

Step-by-step explanation:

Use the half life formula

N=N_0e^{kt} where N is the amount after decay, No is the initial amount, e is Euler's number, k is the decay constant, and t is the time in minutes. For us, the first equation looks like this:

7=12e^{k(70)} and we will solve that for k and then use that value of k in the second equation to find time.

Begin by dividing 7 by 12 to get

\frac{7}{12}=e^{k(70)} Now take the natural log of both sides since the natural log and that e are inverses. The e then disappears:

ln(\frac{7}{12})=k(70)

Plug the left side into your calculator and then set it equal to the right side, giving us:

-.5389965007=70k

Divide both sides by 70 to get the k value of

k = -.00769995

Now the second equation looks like this:

2=12e^{(-.00769995)t where t is our only unknown now that we know k.

Begin by dividing both sides by 12 to get

\frac{1}{6}=e^{-.00769995t and take the natural log of both sides again to eliminate the e:

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Take care of the left side on your calculator to get

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t = 232.697 minutes

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2 years ago
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