Question

What is the probability number selected from the number \[1,2,3,4,5,..........,16\] is a prime number?
A. \[\dfrac{1}{16}\]
B. \[\dfrac{5}{8}\]
C. \[\dfrac{3}{8}\]
D. \[\dfrac{7}{16}\]

Answer 1

Hint: Begin by identifying all conceivable outcomes. Then, from them, determine the prime numbers. To reach the desired result, subtract the numbers of a favorable outcome and the likelihood of getting a prime number.

Complete step-by-step answer:
Given, the numbers are 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and 16
As we know, a general formula for probability is given by
Probability of occurrence of an event \[=\dfrac{\text{Number}\,\text{of}\,\text{favourable}\,\text{cases}}{\text{Total}\,\text{number}\,\text{of}\,\text{possible}\,\text{cases}}\]
The event is that we must choose a number from a list of 16 numbers, with the pick number being a prime number.
As a result, the fortunate circumstance is that the chosen number is a prime number.
From the given 16 numbers, the numbers that are prime numbers are 2,3,5,7,11,13.
Here, Number of favourable cases \[=\] Total number of numbers that are prime number \[=\] 6
Total number of possible cases \[=\] total number of given numbers \[=16\]
Therefore, probability that a number selected is a prime number \[=\dfrac{6}{16}=\dfrac{3}{8}\]
Hence, \[\dfrac{3}{8}\] is the probability that the number selected from the numbers \[1,2,3,4,5,..........,16\] is a prime number.
So, the correct option is “option C”.
So, the correct answer is “Option C”.

Note: To answer such problems, we must first grasp the fundamental concepts of probability and prime numbers. Remember that an event's probability cannot exceed 1 or have a negative fractional value. The numbers that are prime in this situation are those that are divisible by themselves and one. Total possible outcomes include all 16 numbers because, in the case of total possible outcomes, any of them can occur when a number is chosen at random from these 16 numbers.