an urn contains 40 red chips and sixty white chips. six chips are drawn out and discarded, and a seventh is drawn. what is the probability that the seventh chip is red?
Well, let's see. If I were a seventh chip and all my red friends were discarded, I would be feeling pretty blue...or should I say, white?
But let's do the math anyway. There are initially 40 red chips and 60 white chips, making a total of 100 chips. After discarding six chips, there are 94 chips left in the urn.
Since we are interested in the probability of drawing a red chip on the seventh draw, we need to figure out how many red chips are left. Since 6 chips were discarded, only 34 red chips remain.
Therefore, the probability of drawing a red chip on the seventh draw is 34/94. Which, when simplified, is approximately 0.362.
To find the probability that the seventh chip drawn is red, we need to determine the number of red chips remaining in the urn after drawing 6 chips and discarding them.
Step 1: Calculate the total number of chips initially in the urn:
Total number of chips = number of red chips + number of white chips = 40 + 60 = 100 chips
Step 2: Calculate the number of red chips remaining after drawing and discarding 6 chips:
Number of red chips remaining = Total number of red chips - Number of red chips drawn and discarded = 40 - 6 = 34 red chips
Step 3: Calculate the total number of chips remaining in the urn after drawing and discarding 6 chips:
Total number of chips remaining = Total number of chips - Number of chips drawn and discarded = 100 - 6 = 94 chips
Step 4: Calculate the probability that the seventh chip drawn is red:
Probability = Number of red chips remaining / Total number of chips remaining = 34 / 94 ≈ 0.3617
Therefore, the probability that the seventh chip drawn is red is approximately 0.3617 or 36.17%.
To find the probability that the seventh chip drawn is red, we need to first determine the number of red and white chips remaining after the first six chips are drawn and discarded.
Initially, there are 40 red chips and 60 white chips in the urn, for a total of 100 chips.
For the first chip drawn, there are 40 red chips out of 100, so the probability of drawing a red chip is 40/100 or 2/5.
Since the chips are discarded after they are drawn, the number of remaining red and white chips changes for each subsequent draw.
After the first chip is drawn, there are 39 red chips and 60 white chips remaining, for a total of 99 chips.
The probability of drawing a red chip on the second draw is then 39/99, since there are 39 red chips out of the remaining 99 chips.
Similarly, for the third draw, there are 38 red chips and 60 white chips remaining, so the probability of drawing a red chip is 38/98.
Continuing this pattern, after the sixth chip is drawn, there will be 35 red chips and 60 white chips remaining, for a total of 95 chips.
Finally, for the seventh draw, there are 35 red chips and 60 white chips remaining, so the probability of drawing a red chip is 35/95.
Thus, the probability of drawing a red chip on the seventh draw is 35/95.
case 1: all 6 are red. P(red) = 34/94
case 2: 5 reds and 1 blue were drawn. P(red) = 35/94
...
case 7: all 6 are blue: P(red) = 40/94
so, what do you think?