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A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number of the coin is not a prime number, is …..
A. $\dfrac{1}{5}$
B. $\dfrac{3}{5}$
C. $\dfrac{2}{5}$
D. $\dfrac{4}{5}$

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Last updated date: 28th Mar 2024
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MVSAT 2024
Answer
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Hint: We will take the reference of prime numbers and separate prime numbers and composite numbers from 51 to 100. As, we have to find the probability that the number of coins is not a prime number, we will first find the probability that the number is prime and then we will subtract the probability of prime numbers with 1 to get the probability of composite number. The total number of outcomes is already given to us as 50. We have to find the favourable outcomes and then divide it by 50 to get the probability of the prime number.

Complete step-by-step answer:
It is given in the question that a bag contains 50 coins and each coin is marked from 51 to 100 and a coin is picked at random. So, we have to find the probability that the number of the coin is not a prime number. We know that prime numbers are those which have only two factors, first 1 and the second is the number itself. For example, 2, 3, 5, 7 , 11, 13, 17…. etc. Now the prime numbers between 51 and 100 are 53, 59, 61, 67, 71, 73, 79, 83, 87, 97. So, the total number of prime numbers between 51 and 100 are 10. Now, we know that the probability is given as $\dfrac{number\text{ }of\text{ }favourable\text{ }outcomes}{total\text{ }outcomes}$. We will first find the probability that the picked coin is a prime number. So, we will have,
The favoured outcome in this case as = 50, and we know that the total outcome = 10. So,
The probability that the coin is a prime number = $\dfrac{10}{50}\Rightarrow \dfrac{1}{5}$.
Now, we know that the total probability, that is the favoured outcome + unfavoured outcome is equal to 1. So, the probability of the coin not being a prime number can be calculated by subtracting the probability of the coin being a prime number from 1. We know that,
The probability that the coin is a prime number = $\dfrac{1}{5}$.
So, the probability that the coin is not a prime number = $1-\dfrac{1}{5}\Rightarrow \dfrac{5-1}{5}\Rightarrow \dfrac{4}{5}$.
Thus, the probability that the coin is not a prime number is $\dfrac{4}{5}$.
Hence, the correct answer is option D.

Note: Majority of the students forget to notice the word ‘not’ before the prime number and take $\dfrac{1}{5}$ as the answer. The probability of getting prime numbers is $\dfrac{1}{5}$, and it is present in the options also, but it is asked in the question that we have to find the probability of the number being not a prime number. The students can write down all the numbers in order, then strike out the prime numbers and count to get the favourable outcomes of non-prime numbers.