Ask question

Ask question

All categories

1 year ago

12

When a certain basketball player takes his first shot in a game he succeeds with probability 1/2. If he misses his first shot, h

e loses confidence and his second shot will go in with probability 1/3. If he misses his first 2 shots then his third shot will go in with probability 1/4. His success probability goes down further to 1/5 after he misses his first 3 shots. If he misses his first 4 shots then the coach will remove him from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game.
a. Calculate the probability mass function of X.
b. Compute the expected value of X.

1 answer:

Gnom [1K]1 year ago

3 0

Answer:

we are given

basketball player Chauncey Billups of the Detroit Pistons makes free throw shots 88% of the time

so, probability of making shot is

=88%

so, p=0.88

To find the probability of missing first shot and making the second shot

so, we can use formula

probability = p(1-p)

now, we can plug values

we get

So, the probability that he misses his first shot and makes the second is 0.1056........Answer

Step-by-step explanation:

You might be interested in

sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60 : 36 by 1 . Is Sophia c

guapka [62]

Answer:

No multiplying both quantities in the ratio 60 : 36 by 1 would not give the answer .

But multiplying both quantities in the ratio 60 : 36 by 1/6 would solve it.

Step-by-step explanation:

Multiplying any number or ratio by 1 gives the same answer no matter what the expression or how much bigger the number is.This will not give the solution .

If it is multiplied with a fraction like 1/6 that would give the correct answer.

Multiplying it with 1/6 reduces the ratio and gives a better estimate.

A:B

60:36

60*1/6: 36*1/6

10: 6

Meaning that for a total of 16 there are 10 of category A and 6 of category B.

But if we do the same procedure with the answer is same which does not solve the question.

A:B

60:36

60*1: 36*1

60: 36

4 0

2 years ago

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

or

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

$\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1$

$2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7$

$2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6$

4 0

1 year ago

Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of

Flura [38]

$\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+10\,\mathbf k$
$\implies\nabla\cdot\mathbf f(x,y,z)=1+1+0=2$

By the divergence theorem, the surface integral along $S$ is equivalent to the triple integral over the region $R$ bounded by $S$ :

$\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=2\iiint_R\mathrm dV$

Convert to cylindrical coordinates, setting

$\begin{cases}x=r\cos\theta\\y=Y\\z=r\sin\theta\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dY$

The triple integral is then equivalent to

$=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{Y=0}^{Y=2-r\cos\theta}r\,\mathrm dY\,\mathrm dr\,\mathrm\theta$
$=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r(2-r\cos\theta)\,\mathrm dr\,\mathrm\theta$
$=\displaystyle\frac23\int_{\theta=0}^{\theta=2\pi}(3-\cos\theta)\,\mathrm dr\,\mathrm\theta$
$=4\pi$

6 0

2 years ago

Look at the middle 7 in the decimal 0.777. How is its value related to the value of the 7 to its left? To the value of the 7 to

masya89 [10]

Answer:

Value of middle 7 = $\frac{1}{10}$ (value of 7 to the left of the middle 7)

Value of middle 7 = $10$ (value of 7 to the right of the middle 7)

Step-by-step explanation:

7 in the middle of number $0.777$ is equal to $\frac{7}{100}$

7 to the left of the middle 7 is equal to $\frac{7}{10}$

So,

$\frac{7}{100}=(\frac{1}{10}) \frac{7}{10}$

That is value of middle 7 = $\frac{1}{10}$ (value of 7 to the left of the middle 7)

Also,

7 to the right of the middle 7 is equal to $\frac{7}{1000}$

So,

$\frac{7}{100}=(10) \frac{7}{1000}$

That is value of middle 7 = $10$ (value of 7 to the right of the middle 7)

5 0

1 year ago

Dante and Mia have 350 pennies in their piggy banks, altogether. After Dante lost half of his pennies and Mia lost one third of

Alja [10]

350 × 1/2 and 350 × 1/3 I tried :P

5 0

1 year ago