Question

a basket contains two apples and a peach. you randomly pick a piece of fruit to eat. then you pick another piece to eat later. a) {(a1, a1), (a2, a2), (p, p)} b) {(a1, a2), (a1, p), (a2, a1), (a2, p), (p, a1), (p, a2)} c) {(a1, a1), (a1, a2), (a1, p)} d) {(a1, a1), (a1, a2), (a1, p), (a2, a1), (a2, a2), (a2, p), (p, a1), (p, a2), (p, p)}

Explanation:

Step1: List first - pick possibilities

For the first pick, there are 3 options: apple 1 ($A_1$), apple 2 ($A_2$), or peach ($P$).

Step2: List second - pick possibilities for each first - pick

If the first pick is $A_1$, the second pick can be $A_2$ or $P$. If the first pick is $A_2$, the second pick can be $A_1$ or $P$. If the first pick is $P$, the second pick can be $A_1$ or $A_2$. The sample - space is the set of all possible ordered pairs of the two picks. The possible pairs are $(A_1,A_2),(A_1,P),(A_2,A_1),(A_2,P),(P,A_1),(P,A_2)$.

Answer:

B. $\{(A_1,A_2),(A_1,P),(A_2,A_1),(A_2,P),(P,A_1),(P,A_2)\}$