A runner has four different pairs of shoes. If two shoes are selected at random, what is the probability that they will be a matching pair?
Answer: 1/7
Thanks for any help
2018 hsc practice question aye
Do you want an explanation? It's 1 out of 7 because you took a shoe already, and need another shoe to make a pair. The odds of that second shoe matching the one you already picked is 1/7.
I dont understand what "Reiny" means by c(2,8) what is c and why is it in an (x,y) form????
To find the probability of selecting a matching pair of shoes, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways to select two shoes from the four pairs without any restrictions. This can be calculated using the combination formula, which is denoted as "nCr":
nCr = (n!)/[(r!)(n-r)!]
In this case, we have 8 different shoes (4 pairs), and we want to select 2 shoes, so:
Total number of possible outcomes = 8C2
= (8!)/[(2!)(8-2)!]
= (8!)/(2!6!)
= (8*7)/(2*1)
= 28
Now, we need to determine the number of favorable outcomes or the number of ways to select a matching pair. Since there are 4 pairs, we can select any one of the 4 pairs, and there are 2 shoes in each pair, for a total of 2.
Number of favorable outcomes = 4
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability of selecting a matching pair = Number of favorable outcomes / Total number of possible outcomes
= 4 / 28
= 1 / 7
Therefore, the probability of selecting a matching pair of shoes is 1/7.
The number of pairs = C(8,2) = 28
the number of matching pairs = 4
prob of picking a matching pair = 4/28 = 1/7
in the answer given by "." : "The odds of that second shoe matching the one you already picked is 1/7."
They meant to say : The probability of the second shoe matching the one you already picked is 1/7.
If you wanted the odds, then
prob of match = 1/7
prob of no match = 6/7
odds in favour of a match = 1/7 : 6/7
= 1 : 6