There are 36 chocolates in a box, all identically shaped. There 6 are filled with nuts, 14 with caramel, and 16 aresolid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability ofselecting 2 solid chocolates in a row.
A) $\frac { 4 } { 21 }$
B) $\frac { 16 } { 81 }$
C) $\frac { 4 } { 315 }$
D) $\frac { 5 } { 27 }$

Question

There are 36 chocolates in a box, all identically shaped. There 6 are filled with nuts, 14 with caramel, and 16 aresolid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability ofselecting 2 solid chocolates in a row. 
A) $\frac { 4 } { 21 }$
B) $\frac { 16 } { 81 }$
C) $\frac { 4 } { 315 }$
D) $\frac { 5 } { 27 }$

Quizplus · Accepted Answer

The probability of selecting 2 solid chocolates in a row is found by multiplying the probability of selecting a solid chocolate on the first pick by the probability of selecting a solid chocolate on the second pick, after one solid chocolate has already been taken. The probability of picking a solid chocolate first is $ \frac{16}{36} $ or $ \frac{4}{9} $. After taking one solid chocolate, there are 15 solid chocolates left out of 35 chocolates total. So, the probability of picking another solid chocolate is $ \frac{15}{35} $ or $ \frac{3}{7} $. Multiplying these probabilities gives $ \frac{4}{9} \times \frac{3}{7} = \frac{4}{21} $.

There Are 36 Chocolates in a Box, All Identically Shaped 421\frac { 4 } { 21 }214​

There Are 36 Chocolates in a Box, All Identically Shaped $\frac { 4 } { 21 }$