According to the U.S. Bureau of the Census, about 75% of commuters in the United States drive to work alone. Suppose 150 U.S. commuters are randomly sampled. (a) What is the probability that fewer than 101 commuters drive to work alone

Options b and D

Step-by-step explanation:

It's a question of Boolean's algebra

We will find the truth values of each statement p, q, r, and s first.

p : An isosceles triangle has two congruent sides.

Means truth value is True

q ; A right angle measures 90°

Truth value of this statement will be True

r : Four Points are always coplanar.

Truth value of this statement will be False.

s : A decagon has 12 sides

Truth value of the statement will be False.

Now we come to the options.

a. Four points are always coplanar and a right angle measures 90°.

Here "and" means conjunction and truth value of conjuncion of two statements will be true if only both the statements are true.

r        q         r ∧ q

T        T            T

But the truth value is given as false so not the correct option.

b. Four points are always coplanar and a right angle measures 90°.

As we have discussed in option a. truth value of the conjunction is True so this option will be the correct option.

c. Four points are always coplanar or a right angle measures 90°

OR means it's a disjunction and truth value of disjunction is false only when both the statements are False.

r         q        r ∨ q

T        T           T

But the truth value is given as False, so this option is not correct.

d. Four points are always coplanar or a right angle measure 90°

As discussed in option c. Truth value will be True. so this option will be the correct option.

Options b and d are the correct options.