Answer:

And we can find the individual probabilities using the probability mass function
And replacing we got:

Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And for this case we want to find this probability:

And we can find the individual probabilities using the probability mass function
And replacing we got:

If you do 27-12 (which is 15) you add 15 to 13 and 20
Answer:
8 nickels and 9 dimes
Step-by-step explanation:
If all were dimes, the value would be $1.70. It is $0.40 less than that. Changing a dime for a nickel reduces the value by $0.05, so there must have been $0.40/$0.05 = 8 such changes.
There are 8 nickels and 9 dimes.
_____
<em>Check</em>
8 · 0.05 + 9 · 0.10 = 0.40 + 0.90 = 1.30 . . . the answer checks OK