Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips.
A)$\frac { 1 } { 7 }$
B)$\frac { 6 } { 7 }$
C)$\frac { 9 } { 49 }$
D)$\frac { 1 } { 12 }$

Question

Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips. 
A)$\frac { 1 } { 7 }$ 
B)$\frac { 6 } { 7 }$ 
C)$\frac { 9 } { 49 }$ 
D)$\frac { 1 } { 12 }$

Quizplus · Accepted Answer

The probability of drawing the first red chip is $\frac{3}{7}$. After drawing one red chip, there are 2 red chips left out of 6 total chips, so the probability of drawing a second red chip is $\frac{2}{6} = \frac{1}{3}$. Therefore, the probability of both events occurring is $\frac{3}{7} \times \frac{1}{3} = \frac{1}{7}$.

Two Chips Are Drawn at Random and Without Replacement from a Bag