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The ratio of male employees to female employees among the regular

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The ratio of male employees to female employees among the regular  [#permalink]

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New post 22 Oct 2019, 12:20
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The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{7}{12}\)

D) \(\frac{2}{3}\)

E) \(\frac{3}{4}\)

Can someone please provide a comprehensive solution to such problems?
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Re: The ratio of male employees to female employees among the regular  [#permalink]

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New post 22 Oct 2019, 16:28
I thought it's B. Can someone share the official explanation, please? Thanks in advance!
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Re: The ratio of male employees to female employees among the regular  [#permalink]

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New post 22 Oct 2019, 17:38
SPatel1992 wrote:
I thought it's B. Can someone share the official explanation, please? Thanks in advance!



Considering there are total 4 employees then one will be make and 3 will be female.

Number of combination that a male leaves and is replaced by male = (1C1 * 1C1 ) =1

Number of combination that a female leaves and is replaced by female = (3C1 * 2C1 ) =6


Number of combination that anyonye leaves and is replaced by anyone = (4C1 * 3C1 ) =12

Therefore adding male and female combination and dividing by total we get 7/12.

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Re: The ratio of male employees to female employees among the regular  [#permalink]

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New post 23 Oct 2019, 00:19
Imagine the regular staff is : :idontknow: :idontknow: :idontknow: :idk:
and the on call staff is :idontknow: :idk: :idk:

For the 3 on call staff, each has 4 possible candidates from the regular staff to replace, so total possibilities = 4+4+4

Now, let count how many replacements that cause no change in ratio:
the male in the call staff has 3 males in the regular staff to replace = 3
each of the females in the call staff has 1 female to replace = 1+1

so probability = \(\frac{3+1+1}{4+4+4} = \frac{5}{12}\)

(if you increased the number of regular staff, for example 8 instead of 4, the end ratio will be the same :) )
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Re: The ratio of male employees to female employees among the regular  [#permalink]

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New post 31 Oct 2019, 21:53
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anmolmakkarz17 wrote:
The ratio of male employees to female employees among the regular staff at a bookstore is 1:3. In addition to regular staff members, the bookstore retains two female employees and one male employee who are “on call.” If one of the regular staff members is replaced by an “on call” employee, what is the probability that the ratio of male employees to female employees working in the store remains unchanged?

A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{7}{12}\)

D) \(\frac{2}{3}\)

E) \(\frac{3}{4}\)

Can someone please provide a comprehensive solution to such problems?


The probability that a male is selected from regular staff "AND" The probability that a male is selected from on-call staff "OR" The probability that a female is selected from regular staff "AND" The probability that a female is selected from on-call staff.

\(\frac{1}{3}\) * \(\frac{1}{4}\) + \(\frac{2}{3}\) * \(\frac{3}{4}\)

= \(\frac{7}{12}\)
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Re: The ratio of male employees to female employees among the regular   [#permalink] 31 Oct 2019, 21:53
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