Question

50 POINTS

Question 5

The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

Determine P(2 tails).

12.5%
37.5%
50%
75%

Question 6
Which table shows the sample space for spinning the spinner twice?

spinner with 3 equal sections colored yellow, blue, and red


Blue Yellow Red
Red Red Red Red
Blue Blue Blue Blue
Yellow Yellow Yellow Yellow

Blue Yellow Red
Blue Blue, Blue Blue, Yellow Blue, Red
Blue Blue, Blue Blue, Yellow Blue, Red

Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Red, Yellow Blue, Yellow
Yellow Yellow, Red Yellow, Blue Yellow, Blue

Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Blue, Blue Yellow, Blue
Yellow Red, Yellow Blue, Yellow Yellow, Yellow

Question 7
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.

one third
two thirds
two sixths
four ninths

Answer 1

5. (b) 37.5%

6. Table D: {RR, BR, YR; RB, BB, YB; RY, BY, YY}

7. (d) 4/9

Explanation:

You want the probability of tossing two tails in three coin tosses, the sample space for 2 spins of a 3-color spinner, and the probability of drawing 2 Ds from cards {A, D, D} with replacement.

5. 2 Tails

The elements of the sample space containing 2 tails are {HTT, THT, TTH}, so there are 3 possibilities out of 8.

P(2 tails) = 3/8 = 37.5% . . . . . choice B

6. Sample space

The tables of sample space have the colors of one spin labeling columns, and the colors of the other spin labeling rows. The table with the correct body will have {column label, row label} in each cell. This matches the last table, choice D.

7. Double D

The letter D comprises two of the three letters, so its probability on each draw is 2/3. The probability of two such draws in succession is ...

P(D,D) = (2/3)(2/3) = 4/9 . . . . . choice D

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