Assuming that 10% is the probability of a switch being defective (since left-handedness has nothing to do with the problem):
For a binomial distribution, probability(r out of n) = (nCr) (p)^r (q)^(1-r)
p = 10% = 0.1, q = 1 - p = 0.9
r = 2 switches, n = total of 12 switches
probability = (12C2) (0.1)^2 (0.9)^(12-2)
probability = 66(0.1)^2 (0.9)^10
probability = 0.23
This could be an adding fractions problem. We can add the two fractions together and then determine how many miles she walked.
9 1
--- + ----
10 3
First, we need to find a common denominator. It would be 30, since this is the smallest number both 3 and 10 go into.
So, after that, we need to multiply each numerator by the number we needed to multiply our denominator by to get to 30.
So, 10 times 3 equals 30. So, we need to multiply 9 by 3 as well, which is 27.
Our new fraction here would be:
27
----
30
Next, to get 30, we need to multiply 3 by 10 to get 30. So, we also need to multiply 1 by 10, which is 10.
Our new fraction would be:
10
---
30
So lets take a look at our new equation.
27 10
--- + ----
30 30
Lets add them together. Remember the denominators need to stay the same:
37
----
30
Now that we have an improper fraction, we need to simplify it. 37 goes into 30 once, and we have 7 left over.
So, our final answer would be:
1 and 7
---- of a mile.
30
The probability of rolling a 5 and rolling an odd number on a die is independent; rolling a 5 does not influence the probability of rolling an odd number the next time.
King or Jack is mutually exclusive; they cannot both happen at the same time.
Club or Queen is not mutually exclusive; they can happen at the same time.
King or Ace is mutually exclusive; they cannot both happen at the same time.
