Ask question

Ask question

All categories

2 months ago

7

Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A fol

lowed by a 2 from B?

2 answers:

Svet_ta [12.7K]2 months ago

8 0

The chance of first selecting a 4 from Urn A and then a 2 from Urn B is 1/24

Additional details

Probability refers to how likely an event is to happen relative to all possible outcomes.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation (Ordering)

Permutation counts the ways to order a set of items.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination (Choosing)

Combination counts the ways to choose items without regard to order.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let's analyze the problem.

Urn A has balls numbered 1 through 6, totaling 6 balls.

The probability of picking the ball numbered 4 (one ball) from Urn A is:

$P(A) = \boxed{\frac{1}{6}}$

Urn B contains balls numbered 1 through 4, totaling 4 balls.

The probability of drawing the ball numbered 2 (one ball) from Urn B is:

$P(B) = \boxed {\frac{1}{4}}$

Therefore, the overall chance of drawing a 4 from A followed by a 2 from B is:

$P(A \cap B) = P(A) \times P(B)$

$P(A \cap B) = \frac{1}{6} \times \frac{1}{4}$

$P(A \cap B) = \boxed {\frac{1}{24}}$

Related topics

Different Birthdays : brainly.com/question/7567074
Dependent or Independent Events : brainly.com/question/12029535
Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability, Sample Space, Six, Dice, Die, Binomial Distribution, Mean, Variance, Standard Deviation

Svet_ta [12.7K]2 months ago

7 0

Constructing the tree diagram for this scenario, there are 6 options for drawing from Urn A, each followed by 4 options from Urn B.

This yields a total of 6 × 4 = 24 possible outcomes, which can be enumerated as

{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), ..., (6, 3), (6, 4)},

where the first number indicates the draw from Urn A and the second number the draw from Urn B.

The specific outcome (4, 2) is among these 24 possibilities, so its probability equals 1/24.

Alternatively, calculating the probability via the multiplication rule for independent events, the chance of drawing a 4 from Urn A is 1/6 and drawing a 2 from Urn B is 1/4; multiplying these gives 1/24.

Final answer: 1/24

You might be interested in

Consider the graph and equation, y = 3x, that represent Alonso’s walking speed. What relationship is represented by this equatio

tester [12383]

Response:

Explanation in steps:

In this situation, the x-axis indicates the time taken, while the y-axis shows the distance traveled.

4 0

2 months ago

Read 2 more answers

Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,

PIT_PIT [12445]

Answer:

51.15 cm

Step-by-step explanation:

Data provided

Basin has a depth of 40 centimeters

The angle of the sloping sides is 77°

The calculation for the shortest distance from the tip of the cone to its edge is detailed below:-

The angle will be split and is as follows

$\frac{77^\circ}{2}=38.5^\circ$

In the initial triangle, we will apply the "Cosine formula" as follows:-

$\cos 38.5^\circ=\frac{Base}{Hypotenuse}$

$cos 38.5^\circ=\frac{40}{Hypotenuse}$

$\\\\0.782=\frac{40}{Hypotenuse}$

$\\\\Hypotenuse=\frac{40}{0.782}$

$=51.15\ cm$

4 0

1 month ago

How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =

lawyer [12517]

The adjusted equation $g(x)=\frac{1}{x+4}-6$ , indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is $f(x)=\frac{1}{x}$ .

The transformed equation is $g(x)=\frac{1}{x+4}-6$ .

Applying the function transformation rules, it's clear that the parent function $f(x)=\frac{1}{x}$ has been modified into the function $g(x)=\frac{1}{x+4}-6$ .

According to the function transformation rules,

$f(x+b)$ indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

$f(x)-b$ indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation $g(x)=\frac{1}{x+4}-6$ , shows the graph shifted 4 units to the left and 6 units downward.

6 0

2 months ago

Read 2 more answers

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable

Zina [12379]

Answer:

(A) 0.15625

(B) 0.1875

(C) Cannot be determined

Step-by-step explanation:

The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let's denote X as the duration needed for the student to complete the statistics quiz

Thus, X ~ U(32, 64)

The probability density function (PDF) for a uniform distribution is expressed as;

f(X) = $\frac{1}{b-a}$ , a < X < b where a = 32 and b = 64

The cumulative distribution function (CDF) is given by P(X <= x) = $\frac{x-a}{b-a}$

(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)

P(X > 59) = 1 - P(X <= 59) = 1 - $\frac{x-a}{b-a}$ = 1 - $\frac{59-32}{64-32}$ = $1-\frac{27}{32}$ = 0.15625

(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)

P(X <= 43) = $\frac{43-32}{64-32}$ = $\frac{11}{32}$ = 0.34375

P(X < 37) = $\frac{37-32}{64-32}$ = $\frac{5}{32}$ = 0.15625

P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) The probability that a student takes exactly 44.74 minutes to complete the quiz

= P(X = 44.74)

This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.

3 0

1 month ago

Krystal gets paid $750 every two weeks. She wants to save money for next month's rent but she also needs clothes. Does Krystal h

lawyer [12517]

Answer:

How much is the rent? And how many clothes does she want to buy?

Step-by-step explanation:

6 0

1 month ago

Read 2 more answers