Correct answer: \(\frac{3}{5}\)
Explanation:
The total number of balls in the bag is: \[ 4 \, \text{(black balls)} + 6 \, \text{(red balls)} = 10 \, \text{balls} \] The number of red balls is 6. Therefore, the probability of drawing a red ball is: \[ P(\text{red ball}) = \frac{\text{number of red balls}}{\text{total number of balls}} = \frac{6}{10} = \frac{3}{5} \]
Hence, the probability of drawing a red ball is \(\frac{3}{5}\).
Three distinct numbers are selected randomly from the set \( \{1, 2, 3, \dots, 40\} \). If the probability, that the selected numbers are in an increasing G.P. is \( \frac{m}{n} \), where \( \gcd(m, n) = 1 \), then \( m + n \) is equal to:
A board has 16 squares as shown in the figure. Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is: