1. In a basket there are 6 red marbles and 4 blue marbles. What is the probability of drawing a red marble--P(R)?
2. In a basket there are 6 red marbles and 4 blue marbles. Given that you have selected a red marble and have placed it in the basket, what is the probability of drawing a red marble---P(R) ?
3. In a basket there are 6 red marbles and 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 marbles and 4 blue marbles. What is the probability of drawing a red marble on the first try and without replacing it, drawing a blue marble on the second try? P (B|R)=
5. In a basket there are 6 red marbles and 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 the third try without replacement?
6. In a basket there are 6 red marbles and 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 the third 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 300
H only 500
Both 200
Total 1000
P(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, which usually 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 defective and came from company K. P(K and D)=
Now, find the probability of selecting an item that is both defective 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? Prove
14. 90% of grapes are purple P(P)=.90, of which only 5 % have (M) mold (so 95 % of purple have no mold) 10% of grapes are green P(G)=.10, of which only 8% 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 grade Professor frowns 60% P(f) = .60, of which 35% of time gives passing grade Find 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 Black 2 Red Kings 2 Black Kings 2 Red Queens 2 Black Queens
Determine 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 Green On 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 Combinations
18. How many distinct ordered arrangements of 3 objects can be listed from a group of 4 items when order or placement is important?
19. How many arrangements of 3 objects can be listed from a group of 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 be chosen 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 drawer Red socks 4 in the drawer Total socks 7 in the drawer If 4 socks are drawn, find the probability that 2 socks will be red P( 2R).
26. Black socks 3 in a drawer Red socks 4 in the drawer Total socks 7 in the drawer If 4 socks are drawn, find the probability that 1 socks will be black P( 1 B ).
27. Black socks 3 in a drawer Red socks 4 in the drawer Total socks 7 in the drawer If 4 socks are drawn, find the probability that 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 that the profit came from investments A, B, C?
Draw a Decision Tree using the above information:
30. Company chooses Square Ad 35% of the time In which case sales Double 40% Company chooses Rectangular Ad 45% of the time
In 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 probability it is due to S, R, O ads?
Draw a Decision Tree using the above information:
31. Commodity prices Rise 40% of the time In which case Profits come 15% Commodity prices Steady 20% of the time In which case Profits come 35% Commodity Prices Fall 40% of the time In which case Profits come 45% Given that Profits are made, what is the probability that Commodity prices R, S, F?
Draw a Decision Tree using the above information: