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RAS question

A fair die is thrown once. The probability of getting an even number is:

Correct answer: (C) 1/2.

When a fair die is thrown once, the probability of getting an even number is 1/2.

  1. (A)

    2/3

  2. (B)

    1/3

  3. (C)

    1/2

  4. (D)

    1/6

Explanation

A fair die has the outcomes 1, 2, 3, 4, 5 and 6, and NCERT treats these as six equally likely outcomes. The event asked here is not one single number but the collection of even outcomes: 2, 4 and 6. That gives 3 favourable outcomes out of the total 6 possible outcomes. Using the standard probability rule, probability equals favourable outcomes divided by total outcomes, so the probability of getting an even number is 3/6, which reduces to 1/2.

Why the other options are wrong

  • (A) 2/3 would require four favourable outcomes out of six, but the even numbers on a die are only 2, 4 and 6.
  • (B) 1/3 would match two favourable outcomes out of six, whereas the even-number event has three favourable outcomes.
  • (D) 1/6 is the probability of one specified outcome on an equally likely die, not of the three-outcome event of getting an even number.

Concept

This tests the basic probability idea that an event may contain more than one equally likely outcome. It recurs in RAS reasoning because die, coin and card questions quickly check whether candidates can identify the favourable set before applying the formula.

Source

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