A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

Created: 4 years ago | Updated: 3 years ago

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Probashi Kallyan Bank এক্সিকিউটিভ অফিসার (সাধারণ) ১৮.১০.২০১৯ গণিত সম্ভাব্যতা (Probability)

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Given, Red  = 2
 Yellow  =  4
Pink  =  6
 $P r o b a b i l i t y = {1 - (\frac{{}^{2}C_{2}}{{}^{12}C_{2}} + \frac{{}^{4}C_{2}}{{}^{12}C_{2}} + \frac{{}^{6}C_{2}}{{}^{12}C_{2}})} = {1 - (\frac{{}^{2}C_{2} + {}^{4}C_{2} + {}^{6}C_{2}}{{}^{12}C_{2}})} = {1 - (\frac{\frac{2!}{2! (2 - 2)!} + \frac{4!}{2! 94 - 2)!} + \frac{6!}{2! (6 - 2)!}}{\frac{12!}{2! (12 - 2)!}})} = {1 - (\frac{\frac{2}{2 \times 1} + \frac{4 \times 3 \times 2}{2 \times 2} + \frac{6 \times 5 \times 4 \times 3 \times 2}{2 \times 4 \times 3 \times 2}}{\frac{12 \times 11 \times 10!}{2 \times 10!}})} = {1 - (\frac{1 + 6 + 15}{66})} = 1 - \frac{22}{66} = \frac{66 - 22}{66} = \frac{44}{66} = \frac{2}{3}$

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Md Azizur Rahman

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সম্ভাব্যতা (Probability)

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A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

সম্ভাব্যতা (Probability)

Related Question

1. ২০ সদস্যবিশিষ্ট একটি ফুটবল দল থেকে একজন অধিনায়ক ও একজন সহ-অধিনায়ক কতভাগে নির্বাচন করা যাবে?

3. A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo ?

4. In a box , there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green ?

5.
A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss ?

Probashi Kallyan Bank

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A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

সম্ভাব্যতা (Probability)

Related Question

1. ২০ সদস্যবিশিষ্ট একটি ফুটবল দল থেকে একজন অধিনায়ক ও একজন সহ-অধিনায়ক কতভাগে নির্বাচন করা যাবে?

3. A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo ?

4. In a box , there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green ?

5. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss ?

Probashi Kallyan Bank

Promotion

Download Our Mobile Apps

Satt policy

Main Features

Subscribe our newsletter

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5.
A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss ?