A box contains 10 pink rubber bands and 20 brown rubber bands. What is the probability of picking a pink rubber band, putting it back, and then picking another pink rubber band? P(pink and then pink)
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I apologize for any inconvenience. The probability of picking a pink rubber band and then picking another pink rubber band, with replacement, can be calculated by multiplying the individual probabilities.
The probability of picking a pink rubber band on the first draw is 10/30, or 1/3. After replacing the rubber band, the probability of picking another pink rubber band on the second draw is also 1/3.
Therefore, the probability of picking a pink rubber band and then picking another pink rubber band is:
P(pink and then pink) = P(pink) x P(pink | pink)
= (1/3) x (1/3)
= 1/9
So the probability of picking a pink rubber band, putting it back, and then picking another pink rubber band is 1/9.
To calculate the probability of picking a pink rubber band first and then a pink rubber band again, you need to determine the probability of each individual event and then multiply them together.
Step 1: Calculate the probability of picking a pink rubber band first.
There are 10 pink rubber bands in a total of 30 rubber bands in the box. So the probability of picking a pink rubber band first is:
P(pink first) = Number of pink rubber bands / Total number of rubber bands
= 10 / 30
= 1/3
Step 2: Since the rubber band is being put back after the first pick, the total number of rubber bands remains the same for the second pick.
Step 3: Calculate the probability of picking a pink rubber band for the second time.
Since the rubber band was put back after the first pick, the probability of picking another pink rubber band is still:
P(pink second) = Number of pink rubber bands / Total number of rubber bands
= 10 / 30
= 1/3
Step 4: Multiply the individual probabilities together to find the joint probability.
P(pink and then pink) = P(pink first) * P(pink second)
= (1/3) * (1/3)
= 1/9
Therefore, the probability of picking a pink rubber band, putting it back, and then picking another pink rubber band is 1/9.
To find the probability of picking a pink rubber band and then picking another pink rubber band, you need to consider the total number of rubber bands and the number of pink rubber bands.
First, find the probability of picking a pink rubber band on the first draw. There are 10 pink rubber bands out of a total of 30 rubber bands in the box. Therefore, the probability of picking a pink rubber band on the first draw is:
P(pink on first draw) = Number of pink rubber bands / Total number of rubber bands
= 10 / 30
= 1/3 or approximately 0.3333
Since we are putting the first rubber band back, the number of pink rubber bands and the total number of rubber bands remain the same for the second draw.
Therefore, the probability of picking a pink rubber band on the second draw is also 1/3 or approximately 0.3333.
To find the probability of both events happening (picking a pink rubber band and then picking another pink rubber band), you multiply the probabilities.
P(pink and then pink) = P(pink on first draw) * P(pink on second draw)
= (1/3) * (1/3)
= 1/9 or approximately 0.1111
So, the probability of picking a pink rubber band, putting it back, and then picking another pink rubber band is 1/9 or approximately 0.1111.