### Probability and Odds in a University SurveyA poll of 220 students at a university reveals that 80 are taking a lab science course, and 55 are members of the Honors College, while 18 are taking a lab science and are members of the Honors College. Let \( L \) be the event that a student is taking a lab science, and \( H \) be the event that a student is a member of the Honors College. Complete parts (d) through (e) below.#### d) Calculating Specific ProbabilitiesA student is randomly chosen. Find \( P(L \cap H) \) and \( P((L \cap H)^c) \) and explain what each number represents.\[ P(L \cap H) = \](Simplify your answer.)\[ P((L \cap H)^c) = \](Simplify your answer.)**Explanation:**Explain what \( P(L \cap H) \) and \( P((L \cap H)^c) \) represent. Choose the correct answer below.- \( P(L \cap H) \) is the probability a student is taking a lab sciences and is a member of the Honors College. \( P((L \cap H)^c) \) is the probability a student is not taking a lab science or is not a member of the Honors College.- \( P(L \cap H) \) is the probability a student is taking a lab science or is a member of the Honors College. \( P((L \cap H)^c) \) is the probability a student is not taking a lab science or is not a member of the Honors College.- \( P(L \cap H) \) is the probability a student is taking a lab science and is not a member of the Honors College. \( P((L \cap H)^c) \) is the probability a student is not taking a lab science and is not a member of the Honors College.- \( P(L \cap H) \) is the probability a student is taking a lab science and is a member of the Honors College. \( P((L \cap H)^c) \) is the probability a student is not taking a lab science and is not a member of the Honors College.- \( P(L \cap H) \) is the probability a student is taking a lab science and is not a member of the Honors College. \( P((

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A poll of 220 students at a university reveals that 80 are taking a lab science course, and 55 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 the event that a student is a member of the Honors College. Complete parts (a) through (e) bel d. A student is randomly chosen. Find P(LH) and P((LH)) and explain what each number represents. P(LH)-(Simplify your answer) P((LH))-(Simplify your answer.) Explain what P(LH) and P((LH)) represent. Choose the correct answer below OA. PLH) is the probability a student is taking a lab science and is a member of the Honors College. P ((LH) is the probability a student is not taking a lab science or is not a member of the Honors College. OB. PLH) is the probability a student is taking a lab science or is a member of the Honors College. P (LH)) is the probability a student is not taking a lab science or is not a member of the Honors College OC. PLH) is the probability a student is taking a lab science or is a member of the Honors College. P((LH)) is the probability a student is not taking a lab science and is not a member of the Honors College. OD. PLH) is the probability a student is taking a lab science and is a member of the Honors College. P ((LH) is the probability a student is not taking a lab science and is not a member of the Honors College e. Find the odds against each event in parts (c-d) occurring First write an expression for the odds against H. Select all that apply A POH):PO4) Lê PUMP EM PHI The odds dds against H occurring, in lowest terms, are (Type whole numbers) Next find the odds against Hn L'occurring. First write an expression for these odds. Select all that apply □A (1-P((HOL)))PHAL) c. PHAL:(1-PHAL')) EPHAL): (1-P((HOL))) The odds against Hn L' occurring in lowest terms, are 0 (Type whole numbers) Next find the odds against Ln H occurring. First write an expression for these odds. Select all that apply. A PLOH):(1-P(LH)) C. (1-P(OH))) :P(LAH) DE PLOH):PLOH) The odds against LH occurring, in lowest terms, are (Type whole numbers.) The odds against (LH), in lowest terms, are (Type whole numbers.) 8. P):(1-P(H')) D. 1-P(H):P(H) OF PH):P(H') B. (1-PHOL):P(HOL) □D. PHAL):P((HOL)) OF P((HOL)): PHAL") B. PLAH): (1-P(OH))) D. (1-PLOH)): PLOH) OF PLAH:P(LAH)