Question

I got this question wrong and help on how to get the correct answers shown. Thanks!

A poll of 222 students at a university reveals that 78 are taking a lab science course, and 55 are members of the Honors College, while 16 are taking a lab science and are members of the Honors College. Let-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. a. Display this data in a Venn diagram. Choose the correct diagram below. OB. A. C. 18)78 10 10 b. A student is randomly chosen. Find P(L) and PLn H' and explain what each number represents. First determine the formula to use to find P(L). n(L) 13 P(L) (Simplify your answer.) Determine the formula to use to find P(LnH). PLn11 (Simplify your answer.) Explain what P(L) and P(LnH) represent. Choose the correct answer below. A. P(L) is the probability a student is not a member of the Honors College. P(L η H') is the probability a student is taking a lab science or is not a member of the Honors College. B P(L) is the probability a student is taking a lab science. P(L n H') is the probability a student is taking a lab science and is not a member of the Honors College. ° C. P(L) is the probability a student is taking a lab science. P(L η H') is the probability a student is taking a lab science or is not a member of the Honors College. ○ D. P(L) is the probability a student is not a member of the Honors College. P(L n H') is the probability a student is taking a lab science and is not a member of the Honors College.

Answer 1

a) The correct Venn diagram is (C).

b)The probability $P\left ( L \right )=\frac{n\left ( L \right )}{n\left ( S \right )}=\frac{78}{222}=\frac{13}{37}$

The probability is found using the Venn diagram

$P\left ( L\cap H' \right )=\frac{n\left ( L\cap H' \right )}{n\left ( S \right )}=\frac{62}{222}=\frac{31}{111}$

Choice (B) is correct.

c)The probability $P\left ( H \right )=\frac{n\left ( H \right )}{n\left ( S \right )}=\frac{55}{222}$

The probability is found using the Venn diagram

$P\left ( H\cap L' \right )=\frac{n\left ( H\cap L' \right )}{n\left ( S \right )}=\frac{39}{222}=\frac{13}{74}$

Choice (D) is correct.

d)The probability is found using the Venn diagram

$P\left ( L\cap H\right )=\frac{n\left ( L\cap H\right )}{n\left ( S \right )}=\frac{16}{222}=\frac{8}{111}$

$P\left ( \left (L\cap H \right )'\right )=1-P\left (L\cap H \right )=1-\frac{8}{111}=\frac{103}{111}$

Since $P\left ( \left (L\cap H \right )'\right )=P\left ( L'\cup H '\right )$ , the correct choice is (B).

e) (D) and (F) are correct. The odds against H occurring is

(E) and (F) are correct. The odds against $H\cap L'$ occurring is

(C) and (F) are correct.

The odds against $L\cap H$ occurring is

The odds against $\left (L\cap H \right )'$ occurring is