if a tray contain 6 red socks and 4 blue socks . what is the probability that 2 socks , picked will be red

Probability = P(2 red)+P(2 blue)

=6/10*5/9 + 4/10*3/9
=(30+12)/90
=7/15

Question asks P(2 red), so

Probability of first red=6/10
Probability of second red = (6-1)/(10-1)=5/9
By the multiplication rule,
P(2 red)
=6/10*5/9
=30/90
=1/3

6C2÷10C2 = 15÷45=(1÷3)=0.33333...

Well, if you're picking socks from a tray, you better not be using your feet! That would be quite the balancing act! Now, let's get to your question.

To find the probability of picking two red socks, we need to consider the total number of socks and the number of red socks in the tray.

The total number of socks in the tray is 6 red socks plus 4 blue socks, which gives us a total of 10 socks.

Now, the probability of picking a red sock first is 6 out of 10, because there are 6 red socks out of the total 10 socks.

After picking the first red sock, there is one fewer red sock in the tray and one fewer sock overall. So, for the second pick, the probability of picking another red sock is 5 out of 9.

To find the overall probability of picking two red socks, we need to multiply the probability of the first pick (6/10) by the probability of the second pick (5/9):

(6/10) * (5/9) = 30/90 = 1/3

So, the probability of picking two red socks from the tray is 1/3 or approximately 33.33%.

To find the probability of picking 2 red socks out of the total number of socks, you need to calculate the ratio of the number of favorable outcomes (picking 2 red socks) to the total number of possible outcomes (picking any 2 socks).

In this case, there are 6 red socks out of a total of 10 socks (6 red + 4 blue).

To calculate the probability, you can use the formula:
Probability (P) = Number of favorable outcomes / Total number of possible outcomes

Number of favorable outcomes: The number of ways to choose 2 red socks out of the 6 available is given by the combination formula, which is represented as C(n,r) or nCr.
In this case, n represents the total number of red socks (6) and r represents the number of socks to be chosen (2).
Using the combination formula, we get C(6,2) = 6! / (2!(6-2)!) = 15. So there are 15 ways to choose 2 red socks.

Total number of possible outcomes: The total number of ways to choose any 2 socks out of the 10 available is given by the combination formula again.
This time, n represents the total number of socks (10) and r represents the number of socks to be chosen (2).
Using the combination formula, we get C(10,2) = 10! / (2!(10-2)!) = 45. So there are 45 ways to choose any 2 socks.

Now, plug the numbers into the formula:
P = Number of favorable outcomes / Total number of possible outcomes
P = 15 / 45
P ≈ 0.3333

Therefore, the probability of picking 2 red socks from the tray is approximately 0.3333, which can also be expressed as a fraction 1/3 or as a percentage 33.33%.

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