Question

An integer is chosen at random from the first 50 natural numbers. The probability of getting an integer divisible by 4 or 6 is .

Answer 1

The natural number less than or equal to 50 and divisible by 6 are 6, 12, 18, 24, 30, 36, 42, and 48.

Therefore, the total numbers that are divisible by 6 are 8.

Now, the natural numbers less than or equal to 50 and divisible by 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48.

Therefore, the total numbers divisible by 4 are 12.

Now, the numbers divisible by both 4 and 6 are 12, 24, 36, and 48.

Therefore, the total numbers that are divisible by both 4 and 6 are 4.

Number of favorable outcomes = 12 + 8 – 4 = 16

$\therefore \text{Required probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{16}{50}=\frac{8}{25}$