# a bag contains 6 white and 4 black balls .2 balls are drawn at random find the probability that they are of same colour.

### Mohammed

Guys, does anyone know the answer?

get a bag contains 6 white and 4 black balls .2 balls are drawn at random find the probability that they are of same colour. from screen.

## A bag contains 6 white and 4 black balls . 2 balls are drawn at random. Find the probability that they are of same colour.

Click here👆to get an answer to your question ✍️ A bag contains 6 white and 4 black balls . 2 balls are drawn at random. Find the probability that they are of same colour.

Question

## A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.

Medium Open in App Solution Verified by Toppr

Let S be the sample space

Then n(S)= number of ways of drawing 2 balls out of (6+4)=10

⇒ 10 C 2 = 2×1 10×9 =45

Let E= event of getting both balls of same color

Then,n(E)= no of ways (2 balls out of six) or (2 balls out of 4)

= 6 C 2 + 4 C 2 = 2×1 6×5 + 2×1 4×3 =15+6=21 ∴P(E)= n(S) n(E) = 45 21 = 15 7

Was this answer helpful?

202 26

## A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colours, is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colours, is. To learn more, visit BYJU’S.

Home

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colours, is

Question A bag contains 6 white and 4

black balls. Two balls are drawn at random. The probability that they are of the same colours, is

A 115 B 25 C 415 D 715 Open in App Solution

The correct option is **D**

715

**Explanation for the correct option:**

**Step 1. Let assume**

S

**be the sample space**

Then, the number of ways of picking 2 balls out of

(6+4) balls = n(S) = C210 = 10×92×1 ∵Crn = n!(n-r)!r! = 45

**Step 2. Let the event of getting both balls of same color**

= E

then, the number of ways of getting (

2 balls out of 6 white balls) or ( 2 balls out of 4 black balls) = n(E) = C26+C24 = 6×52×1+4×32×1 = 15+6 = 21 ∴

Required probability,

P(E) = n(E)n(S) = 2145 = 715

**Hence,**

**option (D) is Correct.**

Suggest Corrections 0

SIMILAR QUESTIONS

**Q.**A bag contains

6 white and 4 black balls . 2

balls are drawn at random. Find the probability that they are of same colour.

**Q.**A bag contains 3 red, 4 white and 5 blue balls (All balls are different). If two balls are drawn at random, then the probability that they are of different colours is:

**Q.**A bag contains 3 Red, 4 White, and 5 bye balls. All balls are different . Two balls are drawn at random. Probability that they are of different colour is?

**Q.**A bag contains 5 black and 4 white balls. Two balls are drawn at random. The probability that they match is

**Q.**Two balls are drawn from a bag containing

5 white and 7

black balls at random. What is the probability that they would be of different colours?

View More

## A bag contains 6 white and 4 black balls. 2 balls are drawn at random. What is the probability that they are of the same colour?

Answer (1 of 5): 6W 4B 10balls P(2 the same colour)=P(W)P(W)+P(B)P(B) =6/10x5/9 + 4/10x3/9=30/90+12/90 =42/90=7/15

A bag contains 6 white and 4 black balls. 2 balls are drawn at random. What is the probability that they are of the same colour?

Ad by Amazon Web Services (AWS)

AWS is how.

AWS removes the complexity of building, training, and deploying machine learning models at any scale.

Sort Jayanta Mukherjee

B Tech IEE in Instrumentation Engineering, Jadavpur University (Graduated 1990)Author has 12.4K answers and 5.4M answer views2y

There are total (6 + 4) = 10 balls in the bag.

So, if two balls are drawn at random from the bag without replacement, it can be drawn in (10C2) ways = [(10!) / {(8!) * (2!)}] ways = 45 ways.

Now, if two balls drawn are of same colour, that may be either both white or both black balls.

Both white balls may be drawn in (6C2) ways = 15 ways.

Both black balls may be drawn in (4C2) ways = 6 ways.

Thus, probability that both balls drawn are of same colour = {(15 + 6) / 45} = (21 / 45) = (7 / 15) ≈ 0.4667

Related questions

What is the probability that ball having same colour if bag contain 6 white and 4 black. Two balls are drawn at random?

A bag contains 6 white, 4 red and 10 black balls, if two balls are drawn at random, what is the probability of both being black?

A bag contains 8 red balls and 6 white balls. 2 balls are drawn at random. What is the probability that both balls are red in color?

A bag contains 16 white and 24 black balls. 2 balls are drawn at random. What is the probability that they are of the same color?

A bag has 4 white and 3 black balls. 2 balls are drawn randomly. What is the probability of getting a white and a black without replacement?

B.L. Srivastava

Author has 6.4K answers and 4.7M answer views2y

There are total (6w + 4b) = 10 balls in the bag. The 2 balls out of 10 can be selected total in C(10, 2) = 10!/2!.8! = 45 no. of ways. Our event happens if the two drawn balls are either white or black . Now, two white balls out of 6 available can be chosen in C(6, 2) = 6!/2!.4! = 15 no. of ways. Similarly 2 black balls out of 4 black balls can be selected in C(4, 2) = 4!/2!.2! = 6 no. of ways. Hence the required probability of getting 2 balls either white or black = (15 + 6)/45 = 21/45 = 7/15 .

Cliva Cunningham

Works at Self-EmployeesAuthor has 63 answers and 27.1K answer views2y

6W 4B 10balls

P(2 the same colour)=P(W)P(W)+P(B)P(B)

=6/10x5/9 + 4/10x3/9=30/90+12/90

=42/90=7/15 Autodesk-US Sponsored

Looking for the best way to learn AutoCAD?

Get 6 free months of CADLearning with your Autodesk AutoCAD annual subscription.

Learn More Md Shafique Ansari

BA in Mathematics & Science, S.k.m.u university,Dumka,Jharkhand (Graduated 2019)Author has 140 answers and 39.9K answer views2y

Number of white coloured balls = 6.

Number of black coloured balls = 4.

So, number of total balls = 10.

Probability (if balls are white) = 6/10 =3/5.

Probability (if balls are black) = 4/10 = 2/5

I hope you will like it.

Please upvote it. Thanks a lot…. Related questions

A bag contains 2 white, 4 black, and 5 red balls. 3 balls are selected randomly. What is the probability of all 3 balls being in the same colors?

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is black?

A bag contains 11 white and 9 black balls and two balls are drawn at random. What is the probability that both are of the same color?

A bag contains 6 white and 4 black balls. Two balls are drawn randomly without replacement. What is the probability that they are both black?

A bag contains 4 white balls, 5 red balls and 6 black balls. If 2 balls are drawn randomly, what is the probability of getting one white color, the same color and a different color?

Claire Chen

NCTzen at NCT (KPop)Author has 106 answers and 101.8K answer views3y

Related

A bag contains 5 black balls and 6 white balls. Two balls are chosen at random. What is the probability that the chosen balls are of different colours?

firstly, you must consider the probability of drawing a black ball or a white ball separately.

the probability of drawing a black ball is 5/11, a white ball 6/11. if there is no replacement, then:

drawing a black ball, then a white ball: 5/11 x 6/10 = 3/11

drawing a white ball, then a black ball: 6/11 x 5/10 = 3/11

adding the two together (3/11 + 3/11) will bring you to the answer of 6/11, which is the probability of drawing two balls of differing colours.

Steven Smith

Earned 98% or higher in all my math classes at UCMO.Author has 3.3K answers and 6.2M answer views5y

Related

A bag contains 8 white and 3 red balls. If two balls are drawn at random, what is the probability that one is of each colour?

I will assume you do not replace the balls between draws.

There are a couple of ways to do this, you could add the probabilities, or you could use combinatorics (hypergeometric distribution).

If you add the probabilities, then you do it like this:

First get the probability that you get white then red.

There is a probability of 8/11 that the first is white. After that the total balls drops to 10. Therefore, the probability that the second is red in that case is 3/10. Multiply those to get 12/55.

Guys, does anyone know the answer?