Suppose we throw a dice once. Then, which one of the following is/are correct?
(A) The probability of getting a number greater than 4 is \(\frac{1}{3}\).
(B) The probability of getting a number greater than or equal to 4 is \(\frac{1}{3}\).
(C) The probability of getting a number less than or equal to 3 is \(\frac{1}{2}\).
(D) The probability of getting a number less than or equal to 6 is 1.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
The probability of an event is the number of favourable outcomes divided by the total number of outcomes. A die has six faces, so one throw has 6 equally likely outcomes.
(A) The probability of getting a number greater than 4 is \(\frac{1}{3}\). Correct. The numbers greater than 4 are 5 and 6, so 2 of the 6 outcomes are favourable: \(\frac{2}{6}=\frac{1}{3}\).
(B) The probability of getting a number greater than or equal to 4 is \(\frac{1}{3}\). Incorrect. “Greater than or equal to 4” includes 4 itself, so the favourable outcomes are 4, 5 and 6: \(\frac{3}{6}=\frac{1}{2}\), not \(\frac{1}{3}\).
(C) The probability of getting a number less than or equal to 3 is \(\frac{1}{2}\). Correct. The favourable outcomes are 1, 2 and 3: \(\frac{3}{6}=\frac{1}{2}\).
(D) The probability of getting a number less than or equal to 6 is 1. Correct. Every face shows a number from 1 to 6, so all 6 outcomes are favourable. This is a sure event: \(\frac{6}{6}=1\).