A box contains 5 white and 3 black balls. If two balls are drawn at random, what

A box contains 5 white and 3 black balls. If two balls are drawn at random, what is the probability that both are white?

A box contains 5 white and 3 black balls. If two balls are drawn at random, what is the probability that both are white?

Correct Answer: 5/14

Step 1: Count the total number of balls in the box. There are 5 white balls and 3 black balls, so the total is 5 + 3 = 8 balls.
Step 2: Determine the probability of drawing the first white ball. There are 5 white balls out of 8 total balls, so the probability is 5/8.
Step 3: After drawing one white ball, there are now 4 white balls left and a total of 7 balls remaining in the box.
Step 4: Determine the probability of drawing a second white ball. Now, there are 4 white balls out of 7 total balls, so the probability is 4/7.
Step 5: Multiply the probabilities of the two events (drawing the first white ball and then the second white ball). This gives us (5/8) * (4/7).
Step 6: Calculate the result of the multiplication: (5 * 4) / (8 * 7) = 20 / 56.
Step 7: Simplify the fraction 20/56. Both numbers can be divided by 4, resulting in 5/14.

Probability of Independent Events – The question tests the understanding of calculating the probability of drawing two specific outcomes (white balls) from a finite set of outcomes (total balls).
Combinatorial Probability – It involves understanding how to calculate probabilities when drawing without replacement, affecting the total number of outcomes.