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Yuliya22 [10]
2 years ago
6

there are 5 red counters and 3 blue counters in bag A. there are 4 red counters in bag B. Tina takes at random a counter from ea

ch bag. what is the probability that Tina takes two blue counters
Mathematics
1 answer:
mars1129 [50]2 years ago
7 0

Answer:

The probability is 0

Step-by-step explanation:

From the first bag, the total number of counters is 5 + 3 = 8

The probability of taking a blue counter from the first bag is the number of blue counters divided by the total number of counters

Mathematically, we have this as;

3/8

For the second bag, all the counters are red with no blue counter

So the probability of taking a blue counter here is 0

Now, the probability that he takes a blue counter in A and a blue counter in B will

be;

3/8 * 0 = 0

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A coin is being flipped 400 times. What is the probability of it landing on heads at most 170 times, rounded to the nearest tent
lisabon 2012 [21]

Hello!

We have two probabilities we can use; we have 170/400, for our experiment, and 1/2, which is our theoretical probability.

To solve, we just multiply the two probabilities.

\frac{170}{400}(1/2)=0.2125≈21.3

Therefore, we have about a 21.3% chance of this event occurring.

I hope this helps!

8 0
2 years ago
How many different 10 person committees can be selected from a pool of 23 people?
Salsk061 [2.6K]

We're going to be using combination since this question is asking how many different combinations of 10 people can be selected from a set of 23.

We would only use permutation if the order of the people in the committee mattered, which it seems it doesn't.

Formula for combination:

C(n,r)=\dfrac{n!}{(n-r)!r!}

Where n represents the number of objects/people in the set and r represents the number of objects/people being chosen from the set

There are 23 people in the set and 10 people being chosen from the set

C(23,10)=\dfrac{23!}{(23-10)!10!}

=\dfrac{23!}{13!\times10!}

Usually I would prefer solving such fractions by hand instead of a calculator, but factorials can result in large numbers and there is too much multiplication. Using a calculator, we get

=1,144,066

Thus, there are 1,144,066 different 10 person committees that can be selected from a pool of 23 people. Let me know if you need any clarifications, thanks!

~ Padoru

4 0
3 years ago
Read 2 more answers
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which state
ololo11 [35]

Given:

A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20.

To find:

The correct statement for the box plot.

Solution:

Lower quartile is 10 and upper quartile is 15, so the box will go from 10 to 15.

Median of the data set is 12, so a line dividing the box will be at 12.

Minimum value is 4 and lower quartile is 10, so the left whisker will go from 4 to 10.

Upper quartile is 15 and maximum value is 20, so the right whisker will go from 15 to 20.

Therefore, the correct option is B.

8 0
2 years ago
Read 2 more answers
Binomial Expansion/Pascal's triangle. Please help with all of number 5.
Mandarinka [93]
\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}

The rows add up to 1,2,4,8,16, respectively. (Notice they're all powers of 2)

The sum of the numbers in row n is 2^{n-1}.

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When n=1,

(1+x)^1=1+x=\dbinom10+\dbinom11x

so the base case holds. Assume the claim holds for n=k, so that

(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k

Use this to show that it holds for n=k+1.

(1+x)^{k+1}=(1+x)(1+x)^k
(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)
(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}

Notice that

\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}
\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}

So you can write the expansion for n=k+1 as

(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}

and since \dbinom{k+1}0=\dbinom{k+1}{k+1}=1, you have

(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}

and so the claim holds for n=k+1, thus proving the claim overall that

(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n

Setting x=1 gives

(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n

which agrees with the result obtained for part (c).
4 0
3 years ago
..........................
Rainbow [258]
Option A

x+8=-3
x+8-8=-3-8
x=-11


Hope I didn't mess up for your sake!
7 0
3 years ago
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