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 on the coin is not a prime number, is
(a)`1/5`
(b) `3/5`
(c) `2/5`
(d) `4/5`

Options

A. `1/5`
B. `3/5`
C. `2/5`
D. `4/5`

Answer

To solve the problem, we need to find the probability that a randomly picked coin from a bag containing coins numbered from 51 to 100 is not a prime number.

### Step-by-step Solution:

1. **Identify the Total Number of Coins**:
The coins are numbered from 51 to 100. Therefore, the total number of coins is:
\[ 100 - 51 + 1 = 50 \]
So, there are 50 coins in total.

**Hint**: Count the range of numbers from 51 to 100 to find the total number of coins.

2. **Identify Prime Numbers Between 51 and 100**:
We need to find the prime numbers in this range. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers between 51 and 100 are:
- 53
- 59
- 61
- 67
- 71
- 73
- 79
- 83
- 89
- 97

Counting these, we find there are 10 prime numbers.

**Hint**: List out the numbers and check each for primality by testing divisibility.

3. **Calculate the Number of Non-Prime Numbers**:
To find the number of non-prime numbers, we subtract the number of prime numbers from the total number of coins:
\[ \text{Number of Non-Prime Numbers} = \text{Total Coins} - \text{Prime Numbers} = 50 - 10 = 40 \]

**Hint**: Use subtraction to find how many numbers are left after counting the prime numbers.

4. **Calculate the Probability of Picking a Non-Prime Number**:
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Here, the number of favorable outcomes (non-prime numbers) is 40 and the total outcomes (total coins) is 50. Thus, the probability is:
\[ P(\text{Non-Prime}) = \frac{40}{50} = \frac{4}{5} \]

**Hint**: Remember to simplify the fraction if possible.

5. **Conclusion**:
The probability that the number on the coin is not a prime number is \( \frac{4}{5} \).

**Final Answer**: (d) \( \frac{4}{5} \)