Question

A poll of 222 students at a university reveals that 82 are taking a lab science course, and 58 are members of the Honors College, while 15 are taking a lab science and are members of the Honors College. Let Lthe event that a student is taking a lab science, and Hthe 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 OA. ○B. O c 43 15 67 97 97 67 67 b. A student is randomly chosen. Find P(L) and P(LnH) and explain what each number represents. First determine the formula to use to find P(L). P(L)(Simplify your answer.) Determine the formula to use to find P(LnH'). P(Ln H)(Simplify your answer.) Explain what P(L) and P(Ln H') represent. Choose the correct answer below. O A O B. 。C. 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. 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. 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 or is not a member of the Honors College. O D. 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 c. A student is randomly chosen. Find P(H) and P(H nLd explain what each number represents PH(Simplifty your answer.) College PHA L')= □ (Simplify your answer.) Explain what P(H) and P(HnL')represent. Choose the correct answer below. O A O B. ° C. P H is the probability a student is a member of the Honors College. P H n L is the probability a student is a member of the Honors College or is not taking a lab science. P(H) is the probability a student is not taking a lab science. (H η L is the probability a student is a member of the Honors College or is not taking a lab science. P H) Is the probability a student is a member of the Honors College. P H η L is the probability a student is a member of the Honors College and is not taking a lab science. P H is the probability a student is not taking a lab science. P H η L D. is the probability a student is a member of the Honors College and is not taking a lab science The odds against H occurring, in lowest terms, are : LI Type whole numbers.) Next find the odds against HnL' occurring. First write an expression for these odds. Select all that apply. (1-P(H n L')) : P(H n L') A. The odds against L'occurring, in lowest terms, are (Type whole numbers.) Next find the odds against Ln H occurring. First write an expression for these odds. Select all that apply. The odds against L n H occurring, in lowest terms, are Type whole numbers.) The odds against (L nH)', in lowest terms, are (Type whole numbers.)

Answer 1

a) Venn Diagram : Option C)

b)

P(L) = n(L)-82 n(S) 222 111

$P(L\cap H') =P(L) -P(L\cap H)$

82 -15 67

c)

H) n(S) 222 111 n(H) 58 29 P(H) = P(H) =

58 -15 43 うう?

d)

n(Ln H) 15 n(S) 222

15 207 (L H) = 1 222 222

$P(L\cap H)$ and $P\left ((L\cap H) ' \right )$ represents :

Answer: Option C)