A word consists of 9 letters; 5 consonants and 4 vowels. There letters are chosen at random. What is the probability that more than one vowel will be selected?

Created: 4 years ago | Updated: 3 years ago

13/42

5/42

17/42

3/14

Probashi Kallyan Bank এসিস্ট্যান্ট এক্সিকিউটিভ অফিসার (ক্যাশ) ০১. ১১. ২০১৯ গণিত সম্ভাব্যতা (Probability)

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Given, Consonants  = 5
Vowels  =  4
Probability 
 =  $= {1 - (\frac{{}^{5}C_{3}}{{}^{9}C_{3}} + \frac{{}^{5}C_{2} \times {}^{4}C_{1}}{{}^{9}C_{3}})} = {1 - (\frac{\frac{5!}{3! (5 - 3)!}}{\frac{9!}{3! (9 - 3)!}} + \frac{\frac{5!}{2! (5 - 2)!} \times \frac{4!}{1! (4 - 1)!}}{\frac{9!}{3! (9 - 3)!}})} = {1 - (\frac{\frac{5!}{3! 2!}}{\frac{9!}{3! 6!}} + \frac{\frac{5!}{2! 3!} \times \frac{4!}{1! 3!}}{\frac{9!}{3! 6!}})} = {1 - (\frac{\frac{5 \times 4 \times 3!}{2 \times 3!}}{\frac{9 \times 8 \times 7 \times 6!}{2 \times 3 \times 6!}} + \frac{\frac{5 \times 4 \times 3!}{2 \times 3!} \times \frac{4 \times 3!}{3!}}{\frac{9 \times 8 \times 7 \times 6!}{2 \times 3 \times 6!}})} = {1 - (\frac{10}{84} + \frac{10 \times 4}{84})} = (1 - \frac{50}{84}) = (\frac{80 - 50}{84}) = \frac{34}{84} = \frac{17}{42}$

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A word consists of 9 letters; 5 consonants and 4 vowels. There letters are chosen at random. What is the probability that more than one vowel will be selected?

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 ?

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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 ?

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A word consists of 9 letters; 5 consonants and 4 vowels. There letters are chosen at random. What is the probability that more than one vowel will be selected?

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

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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 ?