Pick the correct NOT statement.

For example,

A and B both passed the test

NOT (A and B both passed the test) = at least one did not passed the test

Q1) NOT (A passed the test)*

B passed the test

B failed the test

A passed the test

A failed the test

Q2) NOT (A and B both failed the test)*

A and B both failed the test

A and B both passed the test

A passed the test, but B did not

One of A and B passed , or they both passed

Q3) NOT (A, B, C have the same birthday)*

A, B, C all have the same birthday

A, B, C all have different birthdays

Exactly two kids have the same birthday

Two or three kids have the same birthday

A, B, C may have different birthdays, or two of them have the same birthday

Q4) NOT (all 4 questions have different answers)*

at least 3 questions have the same answer

at least 2 questions have the same answer

all questions have different answers

all questions have the same answer

all 4 questions have no answers

Q5) P(100 bullets are shot at Neo, all missed) = 0.7. What is 0.3?*

P(All 100 bullets hit Neo)

P(exactly 1 bullet hit Neo)

P(exactly 99 bullets hit Neo

P(1 or more bullets hit Neo)

P(1 or more bullets missed Neo)

Q6) Drawing 5 cards,P(all are black AND all are clothed) = 0.2. What is 0.8?*

P(none is block, none is clothed)

P(at least 1 is black, at least 1 is clothed)

P(at least one is red AND at least one is not clothed)

P(at least one is red OR at least one is not clothed, or both)

P(at least one is red OR at least one is not clothed, but not both)

Q7) Drawing 5 cards,P(all are less than 3 OR all are greater than 7, or both) = 0.3. What is 0.7?*

P(no card is within 3 and 7)

P(all cards are within 3 and 7)

P(all but one card is within 3 and 7)

P(exactly one card is within 3 and 7)

P(at least one card is within 3 and 7)

Next:

There are 30 balls in a bag:

10 are red, numbered 0, 1, 2... to 9

10 are blue, numbered 0, 1, 2... to 9

10 are green, numbered 0, 1, 2... to 9

2 balls are randomly picked from the bag. The sequence matters.

For all questions, answer "1 in ___", round to the nearest integer (and no further).

For example, 1 in 1234.5 is 1 in 1235.

Please read the description first. (Q1) P(both balls are red) = ?*

Q2) P(both balls are multiples of 3) = ? (3, 6, 9 only)*

Q3) P(both are red AND both are multiples of 3) = ?

Q4) P(both are not red, AND are both not multiples

Q5) P(both are red, AND are both not multiples of 3) = ?*

Q6) P(both are red, AND not both are multiples of 3) = ? (Hint: "not both" is different from "both not". Complete the NOT ( ) special quiz and you will have a better idea. "not both" means NOT(A B) while "both not" means (A' B').*

Next:

Q1) Why is it wrong to say there are 5! ways to arrange A, A, A, B, C?*

There are 3 AAABC in the 5! permutation

There are 3! AAABC in the 5! permutation

There are 3 AAABC in the 5! permutation

There are 3 AAABC in the 5! permutation

Q2) How many different numbers may be arranged by 1, 1, 1, 2, 3?*

40

30

20

10

Q3) How many different "words" may be spelled by I, I, K, S, S? (does not have to be a real word)*

40

30

20

10

Q4) A Plinko disc is sliding down a very wide board. The "Plinko" box may be reached by going 4 "Left" and 3 "Right", but not necessarily in this order. How many different paths are there in win Plinko?*

50

45

40

35

Q5) How many ways are there to arrange the letters in "management", if the first letter must be the same as the last letter? (e.g. ManageentM)*

226800

80640

20160

5040

next:

Q1) What is the greatest difference between permutation and combination?*

combination is n! / (n-r)! and permutation is n! / (n-r)!r!

In combination, sequence matters. In permutation, sequence does not matter

In combinations, some permutations are identical and counted multiple times

drawing 5 cards from a poker deck, there are more combinations than permutations

Q3) There are 9 magnets on the fridge, numbered 1 to 9. A baby puts three of the magnets in his mouth. How many possible mouthful of magnets are there?*

84

168

504

60480

Q3) There are 9 magnets on the fridge, numbered 1, 1, 1, 2, 3, 4, 5, 6.A child arrange them into a number. How many different numbers are there?*

84

168

504

60480

Q4) Cont. from Q3 (1, 1, 1, 2, 3, 4, 5, 6). An adult puts 9 out of the 9 magnets in her hand. How many different handfuls of magnets are there?*

9

6

3

1

Q5) Cont. from Q3 (1, 1, 1, 2, 3, 4, 5, 6). An adult puts 8 out of the 9 magnets in her hand. How many different handfuls of magnets are there?*

9

6

3

1

Q6) Cont. from Q3 (1, 1, 1, 2, 3, 4, 5, 6). An adult puts 7 out of the 9 magnets in her hand. How many different handfuls of magnets are there? (Hint: organized counting)*

30

20

16

15

14