Q19(i):
A child has a die whose six faces show the letters as given below:

The die is thrown once. What is the probability of getting (i) A?

Solution :

Given: A die has six faces marked with the following letters: A, B, C, D, E, A.

To Find: The probability of getting the letter 'A' when the die is thrown once.

Visual Representation of the Die Faces:

Step 1: Identify the Total Number of Possible Outcomes

The die has 6 faces in total. Each face represents a possible outcome when the die is thrown.

Let $S$ be the sample space of the experiment.

$S = \{A, B, C, D, E, A\}$

The total number of possible outcomes, denoted by $n(S)$, is $6$.

Step 2: Identify the Number of Favorable Outcomes

We are looking for the probability of getting the letter 'A'.

Let $E$ be the event of getting 'A'.

Looking at the sample space $S = \{A, B, C, D, E, A\}$, the letter 'A' appears on the first face and the sixth face.

Therefore, the favorable outcomes are $\{A, A\}$.

The number of favorable outcomes, denoted by $n(E)$, is $2$.

Step 3: Apply the Probability Formula

The theoretical probability of an event $E$ is given by the formula:

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$P(E) = \frac{n(E)}{n(S)}$

Step 4: Calculation

Substitute the values identified in Step 1 and Step 2 into the formula:

$P(A) = \frac{2}{6}$

To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is $2$:

$P(A) = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}$

Final Answer: The probability of getting 'A' is $\frac{1}{3}$.

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