Q.41 A deck of ten cards is given to you as shown below in the figure. One card is
drawn at random from this deck. The probability of selecting a number less than
9 is ____. (to one decimal place)
Question Explanation
A deck has 10 cards, each with a distinct number from 1 to 10.
One card is drawn at random and each card is equally likely to be chosen.
- Total possible outcomes (all cards): {1,2,3,4,5,6,7,8,9,10} → 10 outcomes.
- Favourable outcomes (numbers less than 9): {1,2,3,4,5,6,7,8} → 8 outcomes.
Using the classical definition of probability,
\( P(\text{number}<9) = \frac{\text{favourable outcomes}}{\text{total outcomes}} = \frac{8}{10} = 0.8 \)
Thus, rounded to one decimal place, the probability asked in the question is 0.8.
Step-by-Step Reasoning
- Identify the sample space: All 10 cards form the sample space, so the total number of possible outcomes is 10.
- Identify the event: “Selecting a number less than 9” means selecting any of 1, 2, 3, 4, 5, 6, 7, or 8, giving 8 favourable outcomes.
- Apply the probability formula:
\( P(E) = \frac{n(E)}{n(S)} = \frac{8}{10} = \frac{4}{5} = 0.8 \) - Convert to percentage and decimal place:
\( 0.8 \times 100 = 80\% \) and to one decimal place, the required answer remains 0.8.
Detailed Option Discussion
If this appears as a multiple-choice question, typical options might be:
| Option | Value | Comment |
|---|---|---|
| A | 0.8 | Correct, equals \( \frac{8}{10} \). |
| B | 0.7 | Incorrect; would correspond to 7 favourable cards, not 8. |
| C | 0.9 | Incorrect; would mean 9 cards less than 9, but only numbers 1–8 satisfy the condition. |
| D | 0.2 | Incorrect; this is the probability of selecting a number not less than 9 (i.e., 9 or 10). |
The correct option is the one equal to 0.8, since exactly 8 of the 10 cards show a number less than 9.
SEO-Optimised Introduction
Understanding the probability of selecting a number less than 9 from ten cards is a common requirement in school exams and competitive tests.
This simple card-based probability question helps students practise identifying favourable outcomes, total outcomes and applying the basic probability formula accurately.
