Question

A die is thrown once, a number is noted, then find the probability that it is a prime number.

Answer 1

Hint: A die has 6 faces having dots representing numbers from 1 to 6 on each face. We need to find the favorable outcomes for a prime number to appear so as to calculate its probability to appear when a die is thrown. Use:
\[{\text{Probability}} = \dfrac{{{\text{favorable outcomes}}}}{{{\text{total outcomes}}}}\]

Complete step-by-step answer:
The number of dots present on each face of a die are:
1 , 2 , 3 , 4 , 5 , 6.
Prime numbers among these are: 2 , 3 , 5
[Prime number is a number that is divisible only 1 and itself and not by any other number]
Therefore,
Favorable outcomes = 3
Total outcomes = 6
Substituting these values in the formula of probability, we get:
\[{\text{P(prime number)}} = \dfrac{{{\text{favorable outcomes}}}}{{{\text{total outcomes}}}}\]
 $ = \dfrac{3}{6} $
 $ = \dfrac{1}{2} $
In fraction, it can be expressed as:
 $ = \dfrac{1}{2} = 0.5 $
 $ 0.5 \times 100 = 50\% $
Thus, when a die is thrown once, the probability a prime number appears on the top is $ \dfrac{1}{2}{\text{ or }}50\% $ .

Note: As prime numbers are only divisible by 1 and themselves, they only have 2 factors. The numbers having more than 2 factors are called composite numbers.
Examples of prime numbers include 2 , 3 , 5 , 7 etc. And composite numbers include 6 , 8 , 10 etc. Every number is divisible by 1.
Except 2, the rest of the prime numbers are odd.
Positive integers that are greater than 2, can be expressed as the sum of two prime numbers.
Dice is generally cubical in shape, red in colour and have dots of white colour present on their surface.