Coach Gladney has a bag of 17 colored chips: four are blue, 6 are green, 2 are red and the others are yellow. What is the probability of drawing a blue-chip, replacing it, and then drawing a yellow chip?
4/17 * 5/17
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First draw is 4/17, second is 5/17.
The probability of both is found by multiplying the two values.
To find the probability of drawing a blue chip, replacing it, and then drawing a yellow chip, we first need to determine the total number of chips in the bag.
According to the information given, there are 17 chips in total.
Next, we need to determine the number of blue chips in the bag. The problem states that there are four blue chips.
After that, we need to determine the number of yellow chips in the bag. The problem states that the remaining chips (non-blue, non-green, non-red) are yellow. Since there are 17 chips in total and we know the counts for blue (4), green (6), and red (2), we can subtract these numbers from the total count to get the number of yellow chips. Hence, the number of yellow chips is 17 - 4 - 6 - 2 = 5.
Now, since we are replacing the blue chip after drawing it, the probabilities of drawing a blue chip and a yellow chip on each draw remain constant.
The probability of drawing a blue chip is calculated as the number of blue chips divided by the total number of chips:
Probability of drawing blue chip = Number of blue chips / Total number of chips = 4 / 17.
Similarly, the probability of drawing a yellow chip is calculated as the number of yellow chips divided by the total number of chips:
Probability of drawing yellow chip = Number of yellow chips / Total number of chips = 5 / 17.
Since we are replacing the blue chip after drawing it, we can multiply the probabilities of the independent events to find the probability of drawing a blue chip and then a yellow chip:
Probability of drawing a blue chip and then a yellow chip = Probability of drawing blue chip * Probability of drawing yellow chip = (4 / 17) * (5 / 17).
To find the final probability, we can simplify this multiplication:
Probability of drawing a blue chip and then a yellow chip = 20 / 289.
Therefore, the probability of drawing a blue chip, replacing it, and then drawing a yellow chip is 20/289.