In a group A, there are 7 boys and 3 girls, whilst in another group B,

Question

In a group A, there are 7 boys and 3 girls, whilst in another group B, there are 2 boys and 8 girls. One person is selected at random from each group. What is the probability that both are boys ?

A. 7/50
B. 11/45
C. 19/50
D. 37/90
E. 31/50

chetan2u · Answer

If both are boys, the ways are 7C1*2C1=14
Total ways to select one from each group = 10C1*10C1=100

P= \frac{14}{100}=\frac{7}{50}

GMATinsight · Answer

Probability of selecting aboy from group A  = \frac{7}{7+3} = \frac{7}{10}

Probability of selecting aboy from group B  = \frac{2}{2+8} = \frac{2}{10}

Probability that both events happen simultaneously  = \frac{7}{10}*\frac{2}{10} = \frac{7}{50}

Answer: Option A

MathRevolution · Answer

Group A total: 7 + 3 = 10
Total boys: 7
Total girls: 3

Number of ways to select one person out of 10:  ^{10}{C_1} = 10 
Number of ways to select one boy out of 7:  ^7{C_1} = 7

Group B total: 2 + 8 = 10
Total boys: 2
Total girls: 8

Number of ways to select one person out of 10:  ^{10}{C_1} = 10 
Number of ways to select one boy out of 2:  ^2{C_1} = 2

P(both boys):  \frac{7}{10} * \frac{2}{ 10} = \frac{7}{50}

Answer A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a group A, there are 7 boys and 3 girls, whilst in another group B,

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

In a group A, there are 7 boys and 3 girls, whilst in another group B,

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