there are 7 blue socks,5 red socks,3 green socks and 4 yellow socks in a drawer.
1.find the sample space
2.how many socks should I take out without looking to get a pair of socks
3.what is the probability that the first socks that I draw is red
4.what is the probability that the second socks that I draw will be yellow if I do not replace the first socks
Why would you have an odd number of socks of any color?
2. min = 2, max = 5
3. 7/19
4. 4/(19-1) = ?
1. To find the sample space (S), we need to list all possible outcomes. In this case, an outcome represents a combination of different socks that can be drawn from the drawer.
The sample space is given by S = {blue, red, green, yellow}, where each color represents a different type of sock.
To specify each outcome in the sample space, we need to consider all possible combinations of the socks. Since there are 7 blue socks, 5 red socks, 3 green socks, and 4 yellow socks, the sample space will contain a total of 7 + 5 + 3 + 4 = 19 different outcomes.
2. To determine the minimum number of socks needed to guarantee a pair, we can use the "pigeonhole principle". Since there are 4 different colors of socks, we need to choose at least 5 socks to be certain of obtaining a pair of the same color.
This is because if we take 4 socks, one of each color, it is not guaranteed that any two socks will have the same color. However, when we take the 5th sock, it must match the color of at least one of the previously drawn socks, ensuring a pair.
Therefore, you should take out a minimum of 5 socks without looking to get a pair of socks.
3. The probability of drawing a red sock as the first draw can be calculated by dividing the number of red socks by the total number of socks in the drawer.
In this case, there are 5 red socks out of a total of 7 + 5 + 3 + 4 = 19 socks.
So, the probability of drawing a red sock as the first draw is 5/19.
4. If you do not replace the first sock, then the total number of socks in the drawer for the second draw will be reduced by 1. After the first draw, there will be 18 socks remaining in the drawer.
The probability of drawing a yellow sock on the second draw depends on whether or not a yellow sock was chosen on the first draw.
If a yellow sock was chosen on the first draw, there will be 3 yellow socks remaining in the drawer out of a total of 18 socks. So, the probability of drawing a yellow sock on the second draw, given that a yellow sock was chosen on the first draw, is 3/18.
If a yellow sock was not chosen on the first draw, there will still be 4 yellow socks remaining in the drawer out of a total of 18 socks. So, the probability of drawing a yellow sock on the second draw, given that a yellow sock was not chosen on the first draw, is 4/18.
Considering both possibilities, the overall probability of drawing a yellow sock on the second draw, without replacement, is (3/18) * (5/19) + (4/18) * (14/19), which simplifies to approximately 0.161.