In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl? ?

Finding the "probability that at least one is girl" can be done much easier by subtracting the "probability that none is girl" from 1, since these 2 events are the complement of each other, and either one or the other, but never both, may happen.

consider the tree diagram of the problem, check the picture, each branching represents a birth. The only branch where there is no girl (no g), is 

bbbbbb with a probability of (1-0.534=0.466) per each letter b. 

we know that the probability of a particular branch is the multiplication of the probabilities of each letter in the branch.

so in the case, P(bbbbbb)=

finally, P(at least 1 girl) = 1- P(no girl)=1-P(bbbbbb)=1-0.01=0.99

0.99

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.