Question

A die is thrown. Find the probability of getting:
(A) A number greater then 6 and
(B) A number less than 3.

• A. \(0,\frac{1}{3}\)
• B. \(1,\frac{1}{2}\)
• C. \(\frac{1}{2},0\)
• D. \(\frac{1}{2},\frac{1}{3}\)

Answer 1

The Correct Option is A

To find the probability of specific outcomes when a die is thrown, we start by considering a fair six-sided die, which has the numbers 1 through 6 on its faces. The total number of possible outcomes is 6.

Step-by-Step Solution

1. Probability of Getting a Number Greater Than 6 (P(A)):
   • Since a standard die has numbers from 1 to 6, there are no numbers greater than 6.
   • Therefore, the number of favorable outcomes for this event is 0.
   • Hence, the probability P(A) is calculated as:
     \[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{0}{6} = 0 \]
2. Probability of Getting a Number Less Than 3 (P(B)):
   • The numbers less than 3 are 1 and 2.
   • There are 2 favorable outcomes.
   • Thus, the probability P(B) is calculated as:
     \[ P(B) = \frac{2}{6} = \frac{1}{3} \]

Therefore, the probabilities are:
(A) A number greater than 6: \(0\)
(B) A number less than 3: \(\frac{1}{3}\)