Aptitude Discussion

Q. |
Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl. |

✔ A. |
27/34 |

✖ B. |
25/34 |

✖ C. |
19/34 |

✖ D. |
21/34 |

**Solution:**

Option(**A**) is correct

The events of selection of two person is redefined as (i) first is a girl AND second is a boy OR (ii) first is boy AND second

is a girl OR (iii) first is a girl and second is a girl.

So the required probability:

\(=\left(\dfrac{9}{17}+\dfrac{8}{16}\right)+\left(\dfrac{8}{17}+\dfrac{9}{16}\right)+\left(\dfrac{9}{17}+\dfrac{8}{16}\right)\)

\(=\dfrac{9}{34}+\dfrac{9}{34}+\dfrac{9}{34}\)

\(=\dfrac{27}{34}\)

**Edit:** As pointed by **Brijesh**, final answer has been changed from option (B) to option (A).

**Edit 2:** For a quick alternative solution, check comment by **SHIVAM.**

**Edit 3:** For yet another alternative method using negation approach, check comment by **Shrinivas.**

**Sony**

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**Anonymous**

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the required probability mentioned on the solution is wrong ...

=(9/17+8/16)+(8/17+9/16)+(9/17+8/16)

for me (9/17+8/16) is not equal to 9/34

**Shrinivas**

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ANS = 1- P(No girl is selected)

P(No girl is selected) $= {^8C_2}{ ^{17}C_2}$

$=\dfrac{7}{34}$

Therefore,

ANS $= 1- \dfrac{7}{34}$

$= \dfrac{27}{34}$

**SHIVAM**

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You can also do that,

$\dfrac{{^8C_1} \times {^9C_1}}{{^{17}C_2}} + \dfrac{{^8C_0} \times {^9C_2}}{{^{17}C_2}} = \dfrac{27}{34}$

**Brijesh**

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$\dfrac{9}{34} + \dfrac{9}{34} + \dfrac{9}{34} =\dfrac{25}{34}$? is it?

Isn't it supposed to be $\dfrac{27}{34}$.

**Buggi**

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kya yar itna v mistake mat karo.... ans - 27/34

**Vaibhav**

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Yes, answer is A:27/34

This is combination, not arrangement

either 1 girl and 1 boy or both being a girl

**Priyanka**

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the problem is regarding only selection of applicants not about arrangement. so the ans should be 27/34

**Deepika Jain**

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the answer would be 14

**Ravish**

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ans is $27/34$ cz question says 9 girls and solution says 8 girls ..

**Bis**

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The arrangement is wrong. I think the answer should be $27/34$. Please recheck.

P(at least one girl)=1-P(no girl)

1-P(XX) => 1-(8/17 *7/16) =1-7/34 =27/34