Answer :
Since we only have two possible outcomes here: either fiction or non-fiction books, we are dealing with binomial probability. The formula for this is:
[tex]_nC_x\times p^x\times(1-p)^{n-x}[/tex]where n = the number of trials, x = number of successes, p = probability of a success on an individual trial.
Now, based on the question, here are the information:
the number of trials (n) = 7 random books
probability of getting a fiction book on an individual trial = 45%
probability of getting a non-fiction book on an individual trial (p) = 55%
There are two written successes in the question:
a. 0 non fiction book (x)
b. 1 non fiction book (x)
Let's solve first the probability of getting zero non-fiction books. Let's plug in the given data to the formula above.
[tex]\begin{gathered} _nC_x\times p^x\times(1-p)^{n-x} \\ _7C_0\times0.55^0\times0.45^{7-0} \\ 1\times1\times0.00373669 \\ =0.00373669 \end{gathered}[/tex]The probability of getting zero non-fiction book is 0.00373669.
Let's now solve the probability of getting 1 non-fiction book. x = 1.
[tex]\begin{gathered} _nC_x\times p^x\times(1-p)^{n-x} \\ _7C_1\times0.55^1\times0.45^6 \\ 7\times0.55\times0.008303765 \\ =0.031969 \end{gathered}[/tex]The probability of getting 1 non-fiction book is 0.031969.
So, the probability of getting 0 OR 1 non-fiction book is:
[tex]0.00373669+0.031969=0.0357[/tex]The probability of getting 0 OR 1 non-fiction book is 0.0357.