QUESTION 1
Easy
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.
(i) Draw a tree diagram showing all possible pairs of fruits.
(ii) List the sample space.
(iii) What is the probability of picking one apple and one banana?<>
SOLUTION
1
Note down what is given
Basket A contains 1 apple(\(A\)) and 2 oranges(\(O_1, O_2\))
Basket B contains 1 banana(\(B\)) and 1 mango(\(M\))
One fruit is picked from each basket.
Basket B contains 1 banana(\(B\)) and 1 mango(\(M\))
One fruit is picked from each basket.
2
(i) Draw a tree diagram showing all possible pairs of fruits
Shown in figure
3
(ii) List the sample space
\(S = \{(Apple, Banana),(Apple, Mango),(Orange_1, Banana),(Orange_1, Mango), (Orange_2, Banana), (Orange_2, Mango)\}\)
Or simply,
\(S = \{(A,B),(A,M),(O_1,B),(O_1,M),(O_2,B),(O_2,M)\}\)
Or simply,
\(S = \{(A,B),(A,M),(O_1,B),(O_1,M),(O_2,B),(O_2,M)\}\)
4
(iii) Find probability of picking one apple and one banana
The favourable outcome is (\(Apple, Banana\))
So number of favourable outcomes \(= 1\)
Total number of possible outcomes \(= 6\)
Therefore, \(P(Apple\, and\, Banana) = \frac{1}{6}\)
So number of favourable outcomes \(= 1\)
Total number of possible outcomes \(= 6\)
Therefore, \(P(Apple\, and\, Banana) = \frac{1}{6}\)
Concept Note
A tree diagram is a visual representation used to list all possible outcomes in a multi-step experiment.
A sample space is the complete set of all possible outcomes of an experiment.