The odds of choosing one black ball from an urn are 7 to 13. what is the probability of getting a black ball?

Mathematics

2 answers:

TEA [102]4 years ago

7 0

Answer: $\dfrac{7}{20}$

Step-by-step explanation:

The odds for an event is basically the ratio of the favorable outcomes to the unfavorable outcomes.

Given : The odds of choosing one black ball from an urn are 7 to 13.

i.e. favorable outcomes for getting black ball = 7

i.e. unfavorable outcomes for getting black ball = 13

Now , Total outcomes = favorable outcomes+ unfavorable outcomes

=7+13=20

Then, the probability of getting a black ball $=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$=\dfrac{7}{20}$

Hence, the required probability $=\dfrac{7}{20}$

ycow [4]4 years ago

4 0

I think the answer is 7/13.
Hope this helps.

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Exercise 7.3.5 The following is a Markov (migration) matrix for three locations        1 5 1 5 2 5 2 5 2 5 1 5 2 5 2 5 2

fredd [130]

Answer:

Both get the same results that is,

$\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

Step-by-step explanation:

Given :

$\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

and initial population,

$\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]$

a) - After two times, we will find in each position.

$P_2=[P].[M]^2=[P].[M].[M]$

$M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

$=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]$