coexpennan
2021-08-18
Answered

An urn contains 3 red and 7 black balls.
Players A and B withdraw balls from the urn consecutively until a red ball is selected.
Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn.)

You can still ask an expert for help

Clelioo

Answered 2021-08-19
Author has **88** answers

A wins if the first red ball is drawn 1st, 3rd, 5th, or 7th.

We will calculate the number of events for each first apparition of a red ball.(i.e. a red ball is drawn first, therefore there are (9C2) places in which the other 2 red balls can be placed. In other words, there are (9C2) events in which A wins on the first draw)

E(1)=(9C2)

E(3)=(7C2)

E(5)=(5C2)

E(7)=(3C2)

When the sum up the number of favorable events and divide by the number of total events.

S=(10C3)

E(x): The number of favorable events (position of the first red ball)

S: Total number of events (all possible combinations of the balls)

P(A wins)=$\frac{\left(9C2\right)+\left(7C2\right)+\left(5C2\right)+\left(3C2\right)}{10C3}$

P(A wins)=.05833

We will calculate the number of events for each first apparition of a red ball.(i.e. a red ball is drawn first, therefore there are (9C2) places in which the other 2 red balls can be placed. In other words, there are (9C2) events in which A wins on the first draw)

E(1)=(9C2)

E(3)=(7C2)

E(5)=(5C2)

E(7)=(3C2)

When the sum up the number of favorable events and divide by the number of total events.

S=(10C3)

E(x): The number of favorable events (position of the first red ball)

S: Total number of events (all possible combinations of the balls)

P(A wins)=

P(A wins)=.05833

asked 2020-12-15

A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horixontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with the wood. The iece of wood starts fromrest 4.0 m above the rough bottom (a) Where will this wood eventually come to rest? (b) For the motion from the initial release until the piece of wood comes to rest, what is the total amount of work done by friction?

asked 2020-12-05

A 5.00kg sack of flour is lifted vertically at a constant speed of 3.50m/s through a height of 15.0m. a) How great a force is required? b) How much work is done on the sack by the lifting force? What becomes of this work?

asked 2021-02-18

In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?

asked 2021-01-04

Write in words how to read each of the following out loud.

a.

b.

c.

d.

asked 2022-03-15

If a student jumps straight up to a height of 0.440m, what is his initial speed as it leaves the ground?How long is he in the air?

asked 2021-10-15

Suppose

Is the following statement true?

asked 2021-10-12

The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event

A: student is male and event

B: student has blue eyes.

Copy and complete the two-way table so that events A and B are independent.