According to a september 2008 harris poll, 68% of all american adults have a public library card. the percentages do differ by gender, 62% of males have library cards compared to 73% of females. (a) consider the three probabilities: p(a) = .68, p(a|b) = .62, and p(a|c) = .73. define events a, b, c (b) assuming that half of all americans are males, what is the probability that an american adult is a female who owns a library card. (c) assuming that half of all americans are males, what is the probability that a randomly selected american adult who owns a library card is a female?

a) P(A) is the probability that a randomly selected American adult has a library card.

P(A/B) is the probability that a randomly selected American adult has a library card, given that he is a male.

P(A/C) is the probability that a randomly selected American adult has a library card, given that she is a female.

b) There is a 36.5% probability that an American adult is a female who owns a library card.

c) There is a 53.68% probability that a randomly selected American adult who owns a library card is a female.

Step-by-step explanation:

(a) consider the three probabilities: P(A) = .68, P(A|B) = .62, and P(A|C) = .73.

P(A) is the probability that a randomly selected American adult has a library card.

P(A/B) is the probability that a randomly selected American adult has a library card, given that he is a male.

P(A/C) is the probability that a randomly selected American adult has a library card, given that she is a female.

(b) Assuming that half of all Americans are males, what is the probability that an American adult is a female who owns a library card.

There is a 50% probability that an American adult is a male and a 50% probability that an American adult is a female.

There is a 73% probability that an American adult female owns a library card.

So

There is a 36.5% probability that an American adult is a female who owns a library card.

(c) Assuming that half of all Americans are males, what is the probability that a randomly selected American adult who owns a library card is a female?

68% of all american adults have a library card.

In b), we found that 36.5% are american female adults who own a library card.

So

There is a 53.68% probability that a randomly selected American adult who owns a library card is a female.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

i think it is c, not positive though

step-by-step explanation: