Question

jans jewelry box has two drawers. one drawer contains 3 pairs of rhinestone earrings and 2 pairs of diamond earrings. the other drawer contains 2 gold bracelets and 3 silver bracelets. if jan randomly draws one item from each drawer, what is the probability she draws diamond earrings and a silver bracelet?
a. $\frac{6}{25}$
b. 1
c. $\frac{1}{5}$
d. $\frac{2}{5}$

Explanation:

Step1: Calculate probability of diamond earrings

The first drawer has 3 + 2 = 5 pairs of earrings. The probability of drawing diamond earrings, $P(D)$, is $\frac{2}{5}$ since there are 2 pairs of diamond earrings out of 5 total pairs.

Step2: Calculate probability of silver bracelet

The second drawer has 2+3 = 5 bracelets. The probability of drawing a silver bracelet, $P(S)$, is $\frac{3}{5}$ since there are 3 silver bracelets out of 5 total bracelets.

Step3: Use multiplication rule for independent events

Since the draws from the two drawers are independent events, the probability of both events occurring is $P = P(D)\times P(S)$. So $P=\frac{2}{5}\times\frac{3}{5}=\frac{6}{25}$.

Answer:

A. $\frac{6}{25}$