Can you double-check my work and make any corrections if needed? A poll of 220 students at a university reveals that 89 are taking a lab science course, and 57 are members of the HonorsCollege, while 11 are taking a lab science and are members of the Honors College. Let L= the event that a student is taking alab 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.O A.Oc.в.57 11) 8976 11) 4646 ( 11) 7889 11) 57b. A student is randomly chosen. Find P(L) and P(L NH') and explain what each number represents.First determine the formula to use to find P(L).n(L)P(L) =n(S)89(Simplity your answer.)P(L) =220Determine the formula to use to find P(LNH).P(LNH') =|n(LNH')n(S)39P(L NH') =(Simplify your answer.)110Explain what P(L) and P(L NH') represent. Choose the correct answer below.O A. P(L) is the probability a student is not a member of the Honors College. P(LN H') is the probability a student istaking 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(L N H') is the probability a student is taking a lab scienceor is not a member of the Honors College.C. P(L) is the probability a student is taking a lab science. P(LNH) is the probability a student is taking a lab scienceand is not a member of the Honors CollegeO D. P(L) is the probability a student is not a member of the Honors College. P(LNH') is the probability a student istaking a lab science or is not a member of the Honors College.CA student is randomly chosen. Find P(H) and P(H nL') and explain what each number represents.57P(H) =(Simplify your answer.)220| 23P(H NL') =(Simplity your answer.)110Explain what P(H) and P(H NL') represent. Choose the correct answer below.A. P(H) is the probability a student is a member of the Honors College. P(H nL') is the probability a student isa member of the Honors College and is not taking a lab science.B. P(H) is the probability a student is a member of the Honors College. P(HNL') is the probability a student isa member of the Honors College or is not taking a lab science.OC. P(H) is the probability a student is not taking a lab science. P(H NL') is the probability a student isa member of the Honors College and is not taking a lab science.OD. P(H) is the probability a student is not taking a lab science. (HNL') is the probability a student isa member of the Honors College or is not taking a lab science. d. A student is randomly chosen. Find P(L n H) and P (L N H)') and explain what each number represents.P(L N H) = 20 (Simplify your answer.)19P(LN H)') = 20 (Simplify your answer.)Explain what P(L n H) and P(L N H)') represent. Choose the correct answer below.O A. P(L N H) is the probability a student is taking a lab science or is a member of the Honors College. P(L N H)') isthe probability a student is not taking a lab science and is not a member of the Honors College.B. P(L N H) is the probability a student is taking a lab science or is a member of the Honors College. P(L N H)') isthe probability a student is not taking a lab science or is not a member of the Honors College.C. P(LN H) is the probability a student is taking a lab science and is a member of the Honors College. P (L N H)') isthe probability a student is not taking a lab science and is not a member of the Honors College.OD. P(LN H) is the probability a student is taking a lab science and is a member of the Honors College. P((LN H)') isthe probability a student is not taking a lab science or is not a member of the Honors Cllege.e. Find the odds against each event in parts (c-d) occurringFirst write an expression for the odds against H. Select all that apply.DA. P(H):(1- P(L))OC. P(H):(1- P(H'))] E. P(H'). P(H)OB. 1-P(H): P(H)OD. (1- P(H'): P(H)OF. P(H): P(H')The odds against H occurring, in lowest terms, are 163: 57.(Type whole numbers)Next find the odds against HnL'occurring. First write an expression for these odds. Select all that apply.OA. (1- P(H n L'): P(H n L')OC. P(HNL'):(1- P(H N L')DE. P(HNL'): (1-P((HNL))OB. P(HNL'):P((HnL)')OD. (1-P((HNL')2) P(HO L')F. P((HNL')'): PHn L')The odds against Hn L'occurring, in lowest terms, are (87] 23].Next find the odds against LNH occurring. First write an expression for these odds. Select all that apply.| A. P(LN H)') :P(L N H)OC. P(LN H):(1 - P(L N H))DE. PILNH): P(IL N H)|B. P(LN H): (1-P(L N H'))OD. (1-P(L N H): P(L N H)OF. (1-P(LNH)')) : P(LN H)The odds against Ln H occurring, in lowest terms, are 19 1(Type whole numbers.)The odds against (LN H)', in lowest terms, are 1: 19(Type whole numbers.)

Name: Can you double-check my work and make any corrections if needed? A pol
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Description: Can you double-check my work and make any corrections if needed? A poll of 220 students at a university reveals that 89 are taking a lab science course, and 57 are members of the HonorsCollege, while 11 are taking a lab science and are members of the

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d) The explanation of this part is wrong. Note that P((L∩H)')=P(L'∪H') [using De-morgan's law]So the…