Posted: January 30th, 2023

What is the probability of drawing

1. In a basket there are 6 red marblesand 4 blue marbles.What is the probability of drawinga red marble--P(R)?2. In a basket there are 6 red marblesand 4 blue marbles.Given that you have selected a red marble and have placedit in the basket, what is the probability of drawing a redmarble---P(R) ?3. In a basket there are 6 red marblesand 4 blue marbles.However, what is the probability of selecting a red marble,assuming that you did not replace the original red marble, i.e.,sampling without replacement.4. In a basket there are 6 red marblesand 4 blue marbles.What is the probability of drawing a red marble on the first tryand without replacing it, drawing a blue marble on the second try?P (B|R)=5. In a basket there are 6 red marblesand 4 blue marbles.What is the probability of drawing a red marble on the first try,a blue marble on the second try, and another blue marble on thethird try without replacement?6. In a basket there are 6 red marblesand 4 blue marbles.What is the probability of drawing a red marble on the first try,a blue marble on the second try, and another blue marble on thethird try "with" replacement?7. Observe each of the following, assuming independent events.Given P(A) = 30%, P(B) = 20%,find P(A and B) =8. In a certain laboratory we find the following chemicals:C only 300H only 500Both 200Total 1000P(C) =P(H)=P(B)=Now find P(C or H)=P(C only or H only) =9. If P(A and B and C) = 25% and P(B and C) = 75%Find P(A)=10. If P(A|B) = 20% and P(B) = 80%, find P(A and B) =11. Assume that P(B|A) = 50% ; P(B|A' ) = 10% ; P(A)= 32%:P(A and B)=P(A ' and B)=P(B) =12. A manufacturer buys 80% of its materials from Co.K, whichusually has 4% defective. Company L supplies the other 20%of materials, which usually has 6% defective.Find probability of a defective item if it came from K. P(D|K)=Find probability of a defective item if it came from L. P(D|L)=Find the probability of selecting an item that is both defectiveand came from company K.P(K and D)=Now, find the probability of selecting an item that is bothdefective and came from company K.P(L and D)=Now, find the probability of selecting a defective part.P( D ) =13. Assume that P(B) = 50%; P(A and B)= 20%; and P(A|B) = 40%Are A and B independent? Prove14. 90% of grapes are purple P(P)=.90, of which only5 % have (M) mold (so 95 % of purple have no mold)10% of grapes are green P(G)=.10, of which only8% have mold (so 92% of green have no mold)Find P(M|P)=Find P(M|G)=Find P(P and M)=Find PG and M)=Find P(M)=15. Professor smiles 40% P(s) = .40,of which 70% of time gives passing gradeProfessor frowns 60% P(f) = .60,of which 35% of time gives passing gradeFind P(P|s)=Find P(P|f)=Find P(P and s)=Find P(P and f)=Find P (P)=16. A deck of cards holds the following:26 Red 26 Black2 Red Kings 2 Black Kings2 Red Queens 2 Black QueensDetermine the following card probabilities:Probability of drawing a red card P(R)=Prob of drawing 2 red cards with rep. P(R &R)=Prob of drawing 2 red without rep. P(R & R)=Prob of a red & a black with rep. P(R & B)=Prob of a red & a black without rep. P(R & B)=Probability of drawing a king P(K)=Probability of drawing a queen P(Q)=Probability of drawing a red king P(RK)=Prob of 2 red kings with rep P(RK and RK)=Prob of 2 red kings without rep P(RK and RK)=Prob of king & queen with rep. P(K &Q)=Prob of a king and a queen without rep. P(K and Q)=17. A Box holds 30 marbles: 5 Red, 10 Blue, 15 GreenOn only one draw, find P(R)=On only one draw, find P(B)=On only one draw, find P(G)=Find prob of 2 Green with rep P(2G)=Find prob of 2 Green without rep P(2G)=Find prob of Red & Green with rep.P(R&G)=Find prob of Red&Green without rep.P(R&G)=On one draw, find prob of R or G. P(R or G)=On one draw, find P(R or G or B)=On one draw find P(R&G&B)=Hint: Problems 18, 19, & 20 -- Permutations and Combinations18. How many distinct ordered arrangementsof 3 objects can be listed from a groupof 4 items when order or placement is important?19. How many arrangementsof 3 objects can be listed from a groupof 4 items when order or placement is "not" important?20. Eight trucks are in the parking lot,but only 4 can be driven at any one time.How many samples of 4 trucks can bechosen from the population if:a. The order is important?b. If order is not important?22. Using 2 dice, determine the probability of:a. P (11) =b. P (7) =c. P (5) =d. P ( two 7's in a row)e. P ( a 7 and then a 5)f. P ( a 5 and then a 7)25. Black socks 3 in a drawerRed socks 4 in the drawerTotal socks 7 in the drawerIf 4 socks are drawn, find the probabilitythat 2 socks will be red P( 2R).26. Black socks 3 in a drawerRed socks 4 in the drawerTotal socks 7 in the drawerIf 4 socks are drawn, find the probabilitythat 1 socks will be black P( 1 B ).27. Black socks 3 in a drawerRed socks 4 in the drawerTotal socks 7 in the drawerIf 4 socks are drawn, find the probabilitythat 1 socks will be red P( 1 R ).28. Our medicine supplies come in boxes that are (S)mall, (M)edium, (L)arge.Small boxes are ordered 25% of the time and are damaged (D) 2% of the time.Medium boxes are ordered 35% of the time and are damaged ( D) 5% of the time.Large boxes are ordered 40% of the time and are damaged 3% (D) of the time.Given this information, what are the following probabilities?a. P(D | S)=b. P(D | M)=c. P(D | L)=d. P( S and D)=e. P( M and D)=f. P( L and D)=g. P(D)=h. P(S | D)=i. P(M | D) =j. P(L | D) =Draw a Decision Tree using the above information:29. Investment Advisor recommends Investment A 25% of the time.Investment A is profitable 35% of the time.Investment Advisor recommends Investment B 30% of the time.Investment B is profitable 40% of the time.Investment Advisor recommends Investment C 45% of the time.Investment C is profitable 60% of the time.Given that a profit has been made, what is the probability thatthe profit came from investments A, B, C?Draw a Decision Tree using the above information:30. Company chooses Square Ad 35% of the timeIn which case sales Double 40%Company chooses Rectangular Ad 45% of the timeIn which case sales Double 50%Company chooses Oval ad 20% of the time.In which case sales Double 20%Given that sales had doubled, what is the probabilityit is due to S, R, O ads?Draw a Decision Tree using the above information:31. Commodity prices Rise 40% of the timeIn which case Profits come 15%Commodity prices Steady 20% of the timeIn which case Profits come 35%Commodity Prices Fall 40% of the timeIn which case Profits come 45%Given that Profits are made, what is the probability thatCommodity prices R, S, F?Draw a Decision Tree using the above information:

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