Question

Evan has equal numbers of pop songs,jazz songs, and rock songs loaded on his personal music player. He has it set to play songs on a random shuffle. Suppose Evan is designing a simulation that could be used to estimate the probability that the next two songs to play are both jazz songs.

A)Number cube let 1=pop Let 2=Jazz Let 3=Rock Roll cube four times. repeat.

B) Coin let Heads (H)= Jazz Let Tails (T)= Pop or Rock Toss coin three times. repeat.

C.Random digits Let 1,2,3=Jazz Let 4,5,6=pop Let 7,8,9,0=rock select two random digits. repeat.

D. Number Cube Let 1,2=pop Let 3,4=Jazz Let 5,6=rock roll cube two times repeat.

Answer 1

There are an equal number of pop songs, jazz songs, and rock songs on the player. Hence, to model the system he should use consider that each of these three songs are equally likely to occur.

A) A number cube has six digits from 1 - 6. The probability of each of them occurring is equal. If he labels 1 to pop, 2 to be jazz and 3 to be rock and he rolls the cube four times. Hence, the probability of each of them occurring is no more equal. Also, there will be a large number of repeats required to get an outcome as 1/2 the trials that fall on 4, 5 or 6 will be lost.

B) A coin can have two outcomes, namely a head or a tail, each with an equal probability. Here, there are three events with equal probability to be modeled and hence a coin toss cannot be used for this purpose.

C) Random digits range from 0 to 9. They are grouped such that three of them are assigned to jazz, three are assigned to pop and four are assigned to rock. Thus, the probability of each of the song type is not equal. Hence, even this cannot be used to model the system.

D) A number cube has six digits. If two of these digits are assigned to each of three types, then the probability of each of them occurring becomes 1/3. Thus, this can be used to model the player.

Therefore, the correct answer is D.