A box contains 4 white and 6 black balls. If two balls are drawn at random, what

A box contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are white?

A box contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are white?

Step 1: Count the total number of balls in the box. There are 4 white balls and 6 black balls, so the total is 4 + 6 = 10 balls.
Step 2: Determine the probability of drawing the first white ball. There are 4 white balls out of 10 total balls, so the probability is 4/10.
Step 3: After drawing one white ball, there are now 3 white balls left and a total of 9 balls remaining in the box.
Step 4: Determine the probability of drawing the second white ball. Now, the probability is 3/9.
Step 5: Multiply the probabilities of both events to find the overall probability of drawing 2 white balls: (4/10) * (3/9).
Step 6: Simplify the multiplication: (4 * 3) / (10 * 9) = 12/90.
Step 7: Simplify the fraction 12/90 to its lowest terms, which is 1/15.

Probability of Independent Events – The question tests the understanding of calculating probabilities for dependent events, specifically drawing two balls without replacement.
Combinatorial Counting – It involves understanding how to count the total number of ways to choose items from a set.