Question 1

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Probability in General Aptitude Contexts

Think of probability as a lens for general aptitude tasks: a clean, stepwise approach beats guesswork. This section dissects a classic jar-draw problem, showing how a simple two-step process can be understood through conditional reasoning and a complementary counting view. The aim is to make the logic intuitive and reusable in exams.

Foundations of drawing without replacement

Accepted Answer

Think of the draw as a two-step sequence without replacement. The jar starts with 10 balls: 4 red and 6 blue. The first draw yields red with probability 4/10. If that happens, the second draw has 3 red among 9 remaining balls, giving 3/9. Multiply these probabilities for the final result.

Question 2

Combinatorial view: counting outcomes

Accepted Answer

In a combinatorial view, treat each two-ball draw as an unordered pair. The number of ways to pick two red balls is C(4,2) = 6, while the number of two-ball selections from ten is C(10,2) = 45. The probability remains 6/45, i.e., 2/15, aligning with the earlier product-rule result.

Question 3

Step-by-step solution strategy

Accepted Answer

Begin with framing the scenario: identify the total population and whether draws are with or without replacement. For this jar, there are 10 balls. Decide the method: use the product rule for consecutive draws or count unordered outcomes with combinations. Then compute 4/10 times 3/9, or equivalently 6/45, which equals 2/15.

Question 4

Common pitfalls and intuition

Accepted Answer

One frequent pitfall is treating the two red draws as distinct by order. While order matters in a sequential probability product, the event 'two red' is unordered, so either multiply conditional probabilities or compute combinations. This distinction matters for speed and accuracy in exams.

Question 5

Core insight

Accepted Answer

The probability of drawing two red balls without replacement from a jar of 4 red and 6 blue is 2/15. This result appears consistently whether you use the product rule with conditional probabilities or a combinatorial count of favorable versus total two-ball selections.

Probability of Drawing Two Red Balls

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