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# A certain machine produces toy cars in an infinitely repeating cycle

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Math Expert
Joined: 02 Sep 2009
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A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 11:55
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Difficulty:

55% (hard)

Question Stats:

59% (01:13) correct 41% (01:24) wrong based on 81 sessions

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A certain machine produces toy cars in an infinitely repeating cycle of blue, red, green, yellow and black. If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red?

A. $$\frac{1}{6}$$

B. $$\frac{1}{5}$$

C. $$\frac{1}{3}$$

D. $$\frac{2}{5}$$

E. $$\frac{1}{2}$$

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Posts: 72
Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 13:37
Bunuel wrote:
A certain machine produces toy cars in an infinitely repeating cycle of blue, red, green, yellow and black. If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red?

A. $$\frac{1}{6}$$

B. $$\frac{1}{5}$$

C. $$\frac{1}{3}$$

D. $$\frac{2}{5}$$

E. $$\frac{1}{2}$$

Since we need to select two toy cars at random from consecutively produced 6 cars, the only possible selection will be
(Red,Green,Yellow,Black,Blue,Red)

Therefore the probability of selecting two red cars =2 / 6 = 1/3

Not 100% sure
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Joined: 08 Sep 2016
Posts: 117
Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 15:35
I probably overthink this question too, but I think the answer is C.

The cars are produced in a repeating cycle. In order to ensure that you are able to get 2 cars of the same color, you need to have 2 cycles at a minimum.

Each cycle has 5 cars, so in 2 cycles you will have 10 cars.

The total possibility is 10C2 = choose 2 cars out of 10.

Favorable outcome is 6C2 = choose 2 reds out of 6.

Favorable Outcome/ Total Possibility= 6C2/10C2 = 15/45 = 1/3
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Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 15:37
Bunuel wrote:
A certain machine produces toy cars in an infinitely repeating cycle of blue, red, green, yellow and black. If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red?

A. $$\frac{1}{6}$$
B. $$\frac{1}{5}$$
C. $$\frac{1}{3}$$
D. $$\frac{2}{5}$$
E. $$\frac{1}{2}$$

Cycle 1. blue, red, green, yellow and black Cycle 2. blue, red, green, yellow and black Cycle 3. blue, red, green, yellow and black and on and on....

blue, red, green, yellow and black are 5 cars. For selection for 6 cars set we need to consider two cycles at least.

Example: Blue to Blue will have 6 cars. Red to Red will have 6 cars and on and on....

blue, red, green, yellow, black, blue, red, green, yellow, black....

For each of the colors we have 5 sets with 6 cars each. Now for selecting 6 cars out of which 2 are Red can happen if out of these 5 sets we choose the set which has Red to Red in it. Shown below:

Cycle 1. blue, red, green, yellow and black Cycle 2. blue red, green, yellow and black

So, probability $$\frac{1}{5}$$.

Other way to look at the problem is that we have 5 different cars getting produced in repeating cycle. Any time we pick 6 cars, for sure two cars with same color will be picked. As we have 5 different colors, chances for red to be picked is $$\frac{1}{5}$$.

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Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 16:28
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Bunuel wrote:
A certain machine produces toy cars in an infinitely repeating cycle of blue, red, green, yellow and black. If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red?

A. $$\frac{1}{6}$$

B. $$\frac{1}{5}$$

C. $$\frac{1}{3}$$

D. $$\frac{2}{5}$$

E. $$\frac{1}{2}$$

TOTAL Variants:1st cycle Blue/Red/Green/Yellow/Black

2nd cycle same order:Blue/Red/Green/Yellow/Black : total production :10

Pbt of getting red : 2/10 = 1/5 (B)
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Location: India
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A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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31 May 2018, 23:27
Bunuel wrote:
A certain machine produces toy cars in an infinitely repeating cycle of blue, red, green, yellow and black. If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red?

A. $$\frac{1}{6}$$

B. $$\frac{1}{5}$$

C. $$\frac{1}{3}$$

D. $$\frac{2}{5}$$

E. $$\frac{1}{2}$$

The cars are produced in infinitely repeating cycles of blue, red, green, yellow and black.
We are told that 6 consecutive cars are selected at random. We have been asked to find
the probability that there are 2 red cars. This is possible if the first car is red in color.

Since the car is available in 5 colors, the probability of the first car being red in color is $$\frac{1}{5}$$(Option B)
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Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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01 Jun 2018, 03:00

Solution

Given:
• A certain machine produces toy cars in an infinitely repeating cycle of blue (BU), red (R), green (G), yellow (Y), and black (BL)

To find:
• If 6 consecutively produced cars are selected at random, what is the probability that 2 of the cars selected are red

Approach and Working:
• As the color of the cars follow a specific sequence of 5 definite colors, which is getting repeated infinite times, the following are the possible sequences of the repeating cycles:
o BU, R, G, Y, BL, BU …
o R, G, Y, BL, BU, R …
o G, Y, BL, BU, R, G …
o Y, BL, BU, R, G, Y …
o BL, BU, R, G, Y, BL …
As we can see, these are the 5 possible sequences at which the colors are getting repeated
• Hence, total number of cases = 5

Now, if we observe the possible sequences, in every case the 6th car’s color is getting repeated as the color of the 1st car
Therefore, if 6 consecutively produced cars are selected at random, getting 2 cars selected as R is possible when the 1st color is also R (i.e. R G Y BL BU R …)
• Hence, favorable cases = 1
• Therefore, the required probability = $$\frac{1}{5}$$

Hence, the correct answer is option B.

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Re: A certain machine produces toy cars in an infinitely repeating cycle  [#permalink]

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02 Jun 2018, 15:27
The same colored car is repeated after every 5 cars i.e. every sixth car is the same color. Hence, probability of picking red first = 1/5
If red is picked first, the sixth car will anyway be red.

Hence, B.
Re: A certain machine produces toy cars in an infinitely repeating cycle &nbs [#permalink] 02 Jun 2018, 15:27
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