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

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

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## 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 ​

202 26

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## 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

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## 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?

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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

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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

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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

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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

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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.

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Mohammed 16 day ago

Guys, does anyone know the answer?