Mathematics, 27.06.2020 23:01 fordkenae

There are 7 black balls and 8 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that exactly 1 black ball is drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

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Answer from: truesarah111

0.0718

Step-by-step explanation:

Given that there are 7 black balls and 8 red balls.

Probability of an event E is given as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

The required probability that exactly one black ball is drawn out of 4 drawn balls = Probability of drawing 1 black ball $\times$ Probability of drawing 3 black balls.

First of all, let us see the probability of drawing one black ball:

Number of favorable cases = 7 (Total number of black balls)

Total number of cases = 15 (Total number of black balls and red balls)

$P(Black\ Ball) = \dfrac{7}{15}$

Now, have a look at probability of choosing 3 red balls:

We have to choose 3 red balls out of 8 balls:

Total number of favorable cases = $8_{C_3}$ = 8 $\times 7 \times 6$

Now, one black ball is already chosen, so total 14 balls are left out of which 3 balls are to be chosen.

So, total number of cases = ${14}_{C_3} = 14 \times 13 \times 12$

$P(3\ red \ balls) = \dfrac{8 \times 7 \times 6}{14 \times 13 \times 12}$

The required probability =

$P(Black\ balls) \times P(3\ red\ balls)\\\Rightarrow \dfrac{7}{15} \times \dfrac{8 \times 7 \times 6 }{14 \times 13 \times 12}\\\Rightarrow 0.0718$

So, the required probability is 0.0718.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

Answer: 900°

good luck on your studies! : )

david edward.

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