### Probability and Odds in Education**4. A student is randomly chosen. Find P(L ∩ H) and P((L ∩ H)') and explain what each number represents.****d.**1. **P(L ∩ H) =** `` - **(Simplify your answer.)**2. **P((L ∩ H)') =** `` - **(Simplify your answer.)****Explain what P(L ∩ H) and P((L ∩ H)') represent. Choose the correct answer below.**- [ ] A. P(L ∩ H) is the probability a student is taking a lab science and is a member of the Honors College. P((L ∩ H)') is the probability a student is not taking a lab science or is not a member of the Honors College.- [ ] B. P(L ∩ H) is the probability a student is taking a lab science or is a member of the Honors College. P((L ∩ H)') is the probability a student is not taking a lab science or is not a member of the Honors College.- [ ] C. P(L ∩ H) is the probability a student is taking a lab science or is a member of the Honors College. P((L ∩ H)') is the probability a student is not taking a lab science and is not a member of the Honors College.- [ ] D. P(L ∩ H) is the probability a student is taking a lab science and is a member of the Honors College. P((L ∩ H)') 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 (d-e) occurring.****First, write an expression for the odds against H. Select all that apply.**- [ ] A. P(H'): P(H)- [ ] B. P(H): (1 - P(H'))- [ ] C. P(H): (1 - P(L))- [ ] D. 1 - P(H): P(H)- [ ] E. (1 - P(H)): P(H')- [ ] F. P(H): P(H')**The odds against H occurring, in lowest terms, are:** `__ : __`- *(Type whole numbers.)*---**Next, find the ### Understanding Probability with Venn DiagramsA poll of 220 students at a university reveals that 90 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 (a) through (c) below.#### a. Display this data in a Venn diagram. Choose the correct diagram below.- **Option A:** - Lab Science (L): 72 - Overlap (L and H): 18 - Honors College (H): 37 - Outside Both Sets: 93- **Option B:** - Lab Science (L): 90 - Overlap (L and H): 18 - Honors College (H): 55 - Outside Both Sets: 103- **Option C:** - Lab Science (L): 72 - Overlap (L and H): 18 - Honors College (H): 37 - Outside Both Sets: 135- **Option D:** - Lab Science (L): 52 - Overlap (L and H): 18 - Honors College (H): 37 - Outside Both Sets: 113#### Correct Answer: Option A#### b. A student is randomly chosen. Find \( P(L) \) and \( P(L^c \cap H^c) \) and explain what each number represents.##### First determine the formula to use to find \( P(L) \).\[ P(L) = \frac{\text{Number of students taking a lab science}}{\text{Total number of students}} \]\[ P(L) = \frac{90}{220} \]\[ P(L) (Simplify your answer) \]##### Determine the formula to use to find \( P(L^c \cap H^c) \).\[ P(L^c \cap H^c) = \frac{\text{Number of students not taking a lab science and not in the Honors College}}{\text{Total number of students}} \]\[ P(L^c \cap H^c) = \frac{93

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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 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 А. OD. ов. OC. Q Q Q a b. A student is randomly chosen. Find P(L) and P(LH) 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 P(LH). PLAN PLH)-(Simplify your answer) Explain what P(L) and P(LH) represent. Choose the correct answer below OA. P(L) is the probability a student is not a member of the Honors College. PL H') is the probability a student is taking a lab science or is not a member of the Honors College OB. PL) 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 Honers College OC. P(L) is the probability a student is taking a lab science. P(Ln H') is the probability a student is taking a lab science or 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 and is not a member of the Honors College d. A student is randomly chosen. Find P(H) and P(HNL) and explain what each number represents P(H)-(Simplify your answer) PHAL) (Simplify your answer.) Explain what P(H) and P(HNL) represent. Choose the correct answer below OA. P(H) is the probability a student is a member of the Honors College. P(HNL) is the probability a student is a member of the Honors College or is not taking a lab science. OB. P(H) is the probability a student is not taking a lab science. P(HNL) is the probability a student is a member of the Honors College and is not taking a lab science OC. P(H) is the probability a student is a member of the Honors College. P(HNL) is the probability a student is a 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 is a member of the Honors College or is not taking a lab science. @ ddu