Question 1

We will find all possible combinations of fruits picked from two baskets and then calculate a specific probability.

Step 1 — Draw the tree diagram

Let's list the fruits in each basket. Basket A has one Apple (A) and two Oranges (O). Basket B has one Banana (B) and one Mango (M). We pick one fruit from Basket A first. Then we pick one fruit from Basket B. The tree diagram shows these choices.

The possible pairs are: (Apple, Banana) (Apple, Mango) (Orange, Banana) (Orange, Mango)

Step 2 — List the sample space

The sample space is a list of all possible outcomes. We found these outcomes from our tree diagram. Let's write them as a set.

$S = \{(\text{Apple, Banana}), (\text{Apple, Mango}), (\text{Orange, Banana}), (\text{Orange, Mango})\}$

The total number of outcomes is 4.

Step 3 — Calculate the probability

We want the probability of picking one apple and one banana. Let's identify the favourable outcome. The favourable outcome is (Apple, Banana). There is only 1 favourable outcome. The total number of outcomes is 4. We use the probability formula.

$P(\text{Apple and Banana}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

$P(\text{Apple and Banana}) = \frac{1}{4}$

$\boxed{\frac{1}{4}}$

Answer

(i) Tree Diagram: Basket A /
Apple Orange / \ /
Banana Mango Banana Mango Possible pairs: (Apple, Banana), (Apple, Mango), (Orange, Banana), (Orange, Mango) (ii) Sample Space: S = {(Apple, Banana), (Apple, Mango), (Orange, Banana), (Orange, Mango)} (iii) Probability of picking one apple and one banana = $\frac{1}{4}$