It is a binomial distribution type problem, where the probability under the question is the sum


     P = P(fewer than 8 of 15) = P(0) + P(1) + P(2) + . . .  + P(7) =       (1)


The number of trials is              15;
The indexes of success trials        k = 0,1,2,3, . . . ,7
The probability of success trial     p = 0.53;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The sum  (1)  is a cumulative sum.


Instead of calculating every term of (1) individually and then summing them up, you may use Excel function 

BINOM.DIST(7, 15, 0.53, TRUE)  to calculate the cumulative sum value in one click.


In this way,  you get


    P =  = 0.406524.      ANSWER