There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.

(A) Draw a tree diagram showing all possible pairs of fruits.

(B) List the sample space.

(C) What is the probability of picking one apple and one banana?                                                                   [Page No. 169]

(A) Step 1: Pick one fruit from Basket A (3 choices: Apple, Orange 1, Orange 2)

Step 2: Pick one fruit from Basket B (2 choices: Banana, Mango)

Total possible outcomes $= 3 \times 2 = 6$

Tree Diagram:

(B) $S$= {(Apple, Banana), (Apple, Mango),
(Orange, Banana) , (Orange, Mango),
(Orange, Banana) (Orange, Mango)},
$n(S) = 6$ pairs.

(C) Number of favourable outcome $= 1 \{(Apple, Banana)\}$

Total number of outcome $= 6$

$$P(\text{Apple and Banana}) = \frac{1}{6}$$