A box contains 19 red marbles and 19 green marbles.
Sampling at random from the box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time?
since you are replacing the marble each time , and since most marbles don't have any memory that I know of,
the prob is 19/38 or 1/2
To determine the probability of drawing a red marble on the sixth draw, we can use the concept of independent events and the principle of probability.
Since each draw is done with replacement, it means that the probability of drawing a red marble remains the same for each draw, regardless of the outcome of previous draws. In this case, the probability of drawing a red marble on each individual draw is 19/38, as there are 19 red marbles out of a total of 38 marbles.
Therefore, the probability of drawing a red marble on the sixth draw, given that you have drawn a red marble on the previous five draws, is also 19/38. The previous draws do not affect the probability of drawing a red marble on subsequent draws because each draw is independent.
To calculate this probability, you can simply divide the number of favorable outcomes (drawing a red marble) by the total number of possible outcomes (drawing any marble) and express it as a fraction or decimal. In this case, it is 19 (favorable outcomes) divided by 38 (total possible outcomes), resulting in a probability of 1/2 or 0.5 (or 50% if expressed as a percentage).