Question

A poll of 234 students at a university reveals that 72 are taking a lab science course, and 48 are members of the Honors College, while 18 are taking a lab science and are members of the Honors College. Let L = the event that a student is taking a lab science, and H=the event that a student is a member of the Honors College. Complete parts (a) through (e) below. OA. OB. OC. OD 72 1848 3018) 54 54 18 30 48 1872 96 1321 1321 96. b. A student is randomly chosen. Find P(L) and P(L H') and explain what each number represents. First determine the formula to use to find P(L). P(L) = P(L) = (Simplify your answer.) Determine the formula to use to find PL H'). PKL 0H) = POLO H') = (Simplify your answer.) Explain what P(L) and P( LH') represent. Choose the correct answer below. O A. P(L) is the probability a student is taking a lab science. P(LnH') is the probability a student is taking a lab science and is not a member of the Honors College. O B. P(L) is the probability a student is taking a lab science. P(LnH') is the probability a student is taking a lab science or is not a member of the Honors College. OC. P(L) is the probability a student is not a member of the Honors College. P(L H') is the probability a student is taking a lab science and is not a member of the Honors College. OD. P(L) is the probability a student is not a member of the Honors College. P(L H') is the probability a student is taking a lab science or is not a member of the Honors College.

Answer 1

Answer: (a) Option C is correct. Since

n(L) = 72, n(H) = 48, n( LH) = 18

is true for figure in C.

(b)

$P(L)=\frac{n(L)}{234}=\frac{72}{234}=\frac{4}{13}$$P(L)=\frac{n(L)}{234}=\frac{72}{234}=\frac{4}{13}\\ P(L\cap H')=\frac{n(L\cap H')}{234}=\frac{54}{234}=\frac{3}{13}\\ \color{blue}\left (NOTE: n(L\cap H')=54\text{ is the number of students who have Lab Science and are not memebers of Honors College} \right )$

$\text{ Set }L\cap H' \text{ consists of the students who have Lab Science and are not the memebers of Honors College}\\ \color{red} \text{ Option A is correct}$

(c)

n(H) P(H) = 48/234 234 39 n(HL) 5 P(HNL) 30/234 234 39 Set HOL' consists of the students who are members of Honors College and and are not taking Lab Science Option A is correct

(d)

$P(L\cap H)=\frac{n(L\cap H)}{234}=18/234=\frac{1}{13}\\ P((L\cap H)')=1-P((L\cap H)')=1-\frac{1}{13}=\frac{12}{13}\\ \text{ Set }(L\cap H)'=L'\cup H' \text{ consists of the students who do not have Lab Science or are not memebers of Honors College }\\ \color{red} \text{ Option C is correct}$