Question

1) There are 32 chocolates in a box, all identically shaped. There are 9 filled with nuts, 11 with caramel, and 12 are

Answer 1

answer

$\frac{33}{248}$ ≈ 0.1331 = 13.31 %

first chocolate

the probability of picking a chocolate the first time is $\frac{solid chocolates}{total chocolates}$

there are 12 solid chocolates and 32 total chocolates

$\frac{solid chocolates}{total chocolates}$ = $\frac{12}{32}$ = $\frac{3}{8}$

second chocolate

the probability of picking a chocolate the first time is $\frac{solid chocolates}{total chocolates}$

since we already picked a solid chocolate the first time, there is one less solid chocolate and one less total chocolate

there are 12 - 1 = 11 solid chocolates and 32 - 1 = 21 total chocolates

$\frac{solid chocolates}{total chocolates}$ = $\frac{11}{31}$

total probability

to find the probability of both being solid chocolates, multiply their individual probabilities together

$\frac{3}{8} *\frac{11}{31}$

= $\frac{3 * 11}{8 * 31}$

= $\frac{33}{248}$

≈ 0.1331

= 13.31 %