Question
Asked Mar 6, 2019

An urn contains five red balls and four white balls.  A sample of two balls is selected at random from the urn.  Find the probability that:

a) only red balls are selected

b) at least one white ball is selected

check_circle

Expert Answer

Step 1

Concept of probability:

Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.

The general formula to obtain probability of an event A is,

P(A) = (number of favourable elements for event A)/(Total number of elements in the sample space).

The basic properties of probability are given below:

fullscreen
Step 2

Obtain the probability that at least one white ball is selected.

It is given that an urn contains of five red balls and four white balls.

The number of red balls is n(R) = 5.

The total number of balls or sample size is n(S) = 9.

Here, it is given that a sample of two balls is selected at random from a total of 9 balls.

The probability of drawing a red ball in the first selection is P(R1) = 5/9.

After drawing a red ball in the first selection, there will be 4 red balls and total of 8 balls remained in the urn.

The probability of drawing a red ball in the second selection is P(R2) = 4/8.

The requirement is both the selected balls has to be red in colour.

The probability that only red balls are selected is obtained as 0.2778 from the calculation given below:

fullscreen
Step 3

Obtain the probability that at least one white ball is selected.

The total number of balls or sample size is n(S) = 9.

Here, it is given that a sample of two balls is selected at random from a total of 9 balls.

The number of white balls is n(W) = 4.

The probability of drawing a white ball in the first selection is P(W) = 4/9.

The requirem...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Probability

Other

Related Probability Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: If E(X) = 2 and standard deviation of X is 3, what is E(X2)?

A: Variance of X equals the second central moment about 0 minus the square of first central moment. Sym...

question_answer

Q: Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi villag...

A: Given Thickness measurement of ancient prehistoric Native american pot shards discovered in hopi vil...

question_answer

Q: Bill has three one - piece jump suits, five pairs of work pants and eight work shirts. He wears eith...

A: Bill has 5 pants with each of 8 shirts= 5x8=40.So, Bill has 40 combinations of shirts and pants.

question_answer

Q: Four Hatfields and two McCoys are up for 3 construction jobs in Williamson. What is the probability ...

A: It is provided that, 4 Hatfields and 2 McCoys are up for 3 jobs.So, total possible ways of getting 3...

question_answer

Q: According to national data, 20.7% of burglaries are cleared with arrests. A new detective is assigne...

A: In this question we are going to use Binomial Probability Distribution to get the probability. We ar...

question_answer

Q: A patient is a member of a health plan that has a 20 percent discount from the provider and a 15 per...

A: According to this question, a patient is a member of a health plan and as per the plan patient will ...

question_answer

Q: There are 10c first tier national rugby union teams Argentina, AUstrallia, England France,Ireland, I...

A: (a) The number of ways to choose two team pairing among the ten teams will be:

question_answer

Q: Motors Inc. manufactured 325 cars with automatic transmissions, 216 with power steering, and 89with ...

A: We have given,

question_answer

Q: Recall that we say that a random variable X is in the vector space L^2 if it has finite second momen...

A: Properties of a norm:In order to prove that ||X||2 = √E(X2) is a norm, it must satisfy 3 conditions:...