A large box of vegetables contains 7 tomatoes, 3 heads of lettuce, and 8 onions. A vegetable is chosen at random and then placed back in the box, and a second vegetable is picked. What is the probability of choosing a tomato and an onion?
A) $\frac { 14 } { 81 }$
B) $\frac { 81 } { 972 }$
C) $\frac { 28 } { 81 }$
D) $\frac { 81 } { 81 }$
E) $\frac { 1 } { 324 }$

Question

Quizplus · Accepted Answer

The probability of choosing a tomato first is $\frac{7}{18}$ (since there are 7 tomatoes out of 18 vegetables in total). After replacing the first vegetable, the probability of choosing an onion is $\frac{8}{18}$. Multiplying these probabilities gives the probability of both events happening: $\frac{7}{18} \times \frac{8}{18} = \frac{56}{324} = \frac{14}{81}$.

A Large Box of Vegetables Contains 7 Tomatoes, 3 Heads 1481\frac { 14 } { 81 }8114​

A Large Box of Vegetables Contains 7 Tomatoes, 3 Heads $\frac { 14 } { 81 }$