A family has 5 children, what is the probability that there are 3 boys

Question

A family has 5 children, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 Source: https://www.GMATinsight.com

ichhit · Answer

Probability of a girl or a boy = 1/2 
Total children = 5
Probability = 1/2*1/2*1/2*1/2*1/2----1

Now Seq is BBBGG.

So it can be arranged in 5!/3!*2! Ways. ----2

Taking 1 and 2 together

1/32 * 5!/3!*2! = 10/32 = 5/16

Hence E is the answer

Posted from my mobile device

chetan2u · Answer

each child could be in two ways - B or G so two ways
total ways of the 5 child =  2*2*2*2*2 = 2^5=32

ways 3 out of 5 are B =  5C3=\frac{5!}{3!2!}=10

probability = \frac{10}{32}=\frac{5}{16}

E

fskilnik · Answer

? = P\left( {3B\,\,{	ext{and}}\,\,2G\,\,{	ext{among}}\,\,5\,\,{	ext{children}}} ight)

First Step: evaluate the probability of one "typical" favorable scenario, 
> Say BBBGG :: 1/(2^5) = 1/32

Second Step: check whether all favorable scenarios are EQUIPROBABLE. 
> They are: BBGBG, ... , GGBBB all have this same probability (each one considered separately, of course.)

Third Step: check how many favorable scenarios are there. 
> There are C(5,3) = 10 scenarios, because we have to choose 3 places (among 5) to "put" the letter B. 
Note that C(5,3) = C(5,2) because choosing 3 places (among 5) to "put" B is equivalent to choosing 2 places to "put" G.

Four Step: check if all scenarios of the previous step are MUTUALLY EXCLUSIVE, so that we can ADD their probabilities next! 
> Yes. When (say) BBBGG occurs, BGBBG does not occur... the same applies to any 2 occurrences among the 10 of the Third Step!

Fifth Step: taking into account everything previously considered, 
 ? = C\left( {5,3} ight) \cdot \frac{1}{32} = \frac{10}{32} = \frac{5}{16}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
fskilnik.

exc4libur · Answer

p(boy or girl)=1/2 
 arrangements(BBGGG)=5!/3!2!=10 
 p(BBGGG)=(1/2)^5•10=10/32=5/16

Answer (E)

Mugdho · Answer

GMATinsight  help plz

why does it have to be a case of ordering? question didn’t say anything about order...it simply asked if there are 3 boys and 2 girls...

Posted from my mobile device

MBAHOUSE · Answer

a family has 5 children, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 Source: https://www.GMATinsight.com

m7runner · Answer

I have the same question as well. Why should there be ordering? IMO, the answer must be  \frac{1}{32}  as this would be logical. I think there must be additional information in the question so that an "ordering" sequence should be initiated?

Bunuel ,  BrentGMATPrepNow ,  JeffTargetTestPrep ,  ScottTargetTestPrep ,  KarishmaB : could you help here please?

Bunuel · Answer

There are 5 children XXXXX, each of them has 2 options, either a boy or a girl, so there are a total of 2*2*2*2*2 = 32 different cases:
BBBBB
BBBBG
BBBGB
BBGBB
BGBBB
GBBBB
BBBGG
...

The cases when there are 3 boys and 2 girls are cases with all arrangements of BBBGG, which is 5!/(3!2!).

HarishD · Answer

A family has 5 children, what is the probability that there are 3 boys and 2 girls among the children?

Answer: BBBGG (can be arranged in 5!/(3!*2!) = 10, 3 boys and 2 girls

Probability: (1/2)(1/2)(1/2)(1/2)(1/2)(1/2)*arrangements i.e 10
 answer: 5/16 (E)

nischaysetthi · Answer

For  every trial , we have  'two'  possibilities, i.e., either a girl or a boy. There are ' five'  trials. Hence , we can take total as =  2^5

Out of five trials, any two of them are boys. Therefore the number of ways of selecting two trials out of five is  5C2
  (It should be noted that if we select trials for boys, rest of the trials automatically are left for girls.)
 
so if we calculate required number of probability of boys. it will be precisely our answer.

The probability is : (5C2)/2^5 =10/32 = 5/16

A family has 5 children, what is the probability that there are 3 boys

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A family has 5 children, what is the probability that there are 3 boys

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards