Problem 10 - Set 2 - Try Out - General Reasoning - SNBT

A child takes fruits from two different boxes. The composition of fruits in each box is as follows:

Box 1	Box 2	Fruit Type
$1$	$4$	Large apple
$2$	$2$	Small apple
$4$	$3$	Large orange
$5$	$3$	Small orange

If a child takes one fruit from Box 1 and one fruit from Box 2, which combination is the most likely result?

Explanation

First, let's calculate the total number of fruits in each box:

Box 1: $1 + 2 + 4 + 5 = 12$ fruits.
Box 2: $4 + 2 + 3 + 3 = 12$ fruits.
Total Possibilities: $12 \times 12 = 144$ combinations.

We will calculate the probability for each option. Recall that the probability of independent events occurring together is the product of their individual probabilities.

Event	Calculation	Result
2 Large Apples	$\frac{1}{12} \times \frac{4}{12}$	$\frac{4}{144}$
2 Small Apples	$\frac{2}{12} \times \frac{2}{12}$	$\frac{4}{144}$
2 Large Oranges	$\frac{4}{12} \times \frac{3}{12}$	$\frac{12}{144}$
2 Small Oranges	$\frac{5}{12} \times \frac{3}{12}$	$\frac{15}{144}$
1 Large Apple & 1 Small Orange	$(\frac{1}{12} \times \frac{3}{12}) + (\frac{5}{12} \times \frac{4}{12})$	$\frac{23}{144}$

For the event 1 Large Apple & 1 Small Orange, there are two possible ways to obtain it:

Large Apple from Box 1 and Small Orange from Box 2 ( $\frac{1}{12} \times \frac{3}{12}$ ).

Small Orange from Box 1 and Large Apple from Box 2 ( $\frac{5}{12} \times \frac{4}{12}$ ).

These two probabilities are added together.

From the table above, we can see that the highest probability is obtaining 1 large apple and 1 small orange with a probability of $\frac{23}{144}$ .

Thus, the most likely result is 1 large apple and 1 small orange.

Command Palette

Number 10

Explanation