Peter selects a sock from his drawer. The sock is black. There are 4 white socks, 7 blue socks, and 12 black socks left in the drawer. He selects a second sock from the drawer without looking. Is it likely that peter selects a sock of the same color? Explain your reasoning
7th-grade math " Use Theoretical Probability and Proportional Reasoning to Make Predictions"
What do you think?
To determine whether it is likely that Peter selects a sock of the same color on his second draw, we can use theoretical probability, which is a mathematical concept that helps us make predictions based on the likelihood of an event occurring.
First, let's determine the total number of socks left in the drawer after Peter's first draw. Initially, the drawer contained 4 white socks, 7 blue socks, and 12 black socks. Since Peter has already selected one sock, we need to subtract that from the total number of socks: 4 white socks + 7 blue socks + 12 black socks - 1 sock = 23 socks.
Now, let's calculate the probability of Peter selecting a sock of the same color on his second draw. There are two scenarios to consider:
1. If Peter selects a white sock on his first draw, there would be 3 white socks left in the drawer out of the remaining 23 socks. So, the probability of selecting a white sock on the second draw after selecting a white sock on the first draw is 3/23.
2. If Peter selects a blue sock on his first draw, there would be 6 blue socks left in the drawer out of the remaining 23 socks. Therefore, the probability of selecting a blue sock on the second draw after selecting a blue sock on the first draw is 6/23.
3. Finally, if Peter selects a black sock on his first draw, there would be 11 black socks left in the drawer out of the remaining 23 socks. Hence, the probability of selecting a black sock on the second draw after selecting a black sock on the first draw is 11/23.
To determine the overall probability of selecting a sock of the same color on the second draw, we can sum up the individual probabilities:
Probability of selecting a white sock first and then white again: 3/23
Probability of selecting a blue sock first and then blue again: 6/23
Probability of selecting a black sock first and then black again: 11/23
Adding these probabilities together, we get: 3/23 + 6/23 + 11/23 = 20/23.
So, the probability of Peter selecting a sock of the same color on his second draw is 20/23 or approximately 0.87.
Based on the calculation, it is likely that Peter selects a sock of the same color on his second draw.