Question

The probability of getting an even number on spinning the wheel is \[\dfrac{1}{2}\]and that of a prime number\[\dfrac{4}{6}\]. What could be the missing number on the wheel?

A.1
B.2
C.4
D.9

Answer 1

Hint: Hint: The even number is the number that leaves a remainder of 0 when it is divisible by 2, and the prime number is defined as that the number which is divisible by both 1 and itself only. In this solution, firstly find the number of even and prime numbers then we can get an idea to guess the number whether it is an even number or prime number and there may be a chance of both.

Complete step-by-step answer:
The probability of getting an even number on spinning the wheel is \[\dfrac{1}{2}\].
The probability of getting a prime number on spinning the wheel is \[\dfrac{4}{6} = \dfrac{2}{3}\].
The number of even numbers in the wheel is 2.
The number of prime numbers in the wheel is 3.
The total number of numbers except the missing number is 6.
Now, the number of even numbers in the wheel could be,
 \[\dfrac{1}{2} \times 6 = 3\]
We know that the number of prime numbers in the wheel could be,
 \[\dfrac{2}{3} \times 6 = 4\]
It means, out of 6 slots with missing numbers in the wheel, the 3 are even numbers and 4 are prime numbers, where the last or missing number could be both even and prime number. So, the 2 is the only number that can be even and prime at the same time.
The schematic diagram of the wheel is as follows:

Therefore, the number 2 is the missing number that could be both even and prime number both
So, the correct answer is “Option B”.

Note: In the solution, the even number and prime numbers play key roles, so come to know the difference between them. Then it could be easy to find the missing number in the wheel. Don’t get confused between even and prime numbers while defining them, to separate the numbers in the wheel into two sections.