A certain machine produces toy cars in an infinitely repeating cycle

Question

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. \(\frac{1}{2}\)

A.  \frac{1}{6}

B.  \frac{1}{5}

C.  \frac{1}{3}

D.  \frac{2}{5}

E.  \frac{1}{2}

zishu912 · Answer

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

Funsho84 · Answer

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

seed · Answer

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} .

Answer: (B).

alphastallion · Answer

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)

pushpitkc · Answer

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)

EgmatQuantExpert · Answer

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.

Answer: B

US09 · Answer

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.

CEdward · Answer

P(2 reds) = ?

Re-phrased, the question is asking us what is the probability of picking a red on the first and last attempt:

R G Y Bl Blu R <--- This is the only possible way that we will get 2 reds given that 6 are chosen

Now, since there are 5 colors, the denominator is 5.

P(2 reds) = 1/5

Answer is B.

ParitoshRawat99 · Answer

Imagine it like a question where 6 places need to be filled by available number of cars of 5 types.

Total scenarios: 1st space can be filled in 5 ways, 2nd place can be filled in 4 ways, 3rd place can be filled in 3 ways, 4th place can be filled in 2 ways, 5th place can be filled in 1 way.

The 6th place would automatically get filled in 1 way by the same coloured car which takes the initial space.

Thus, total ways = 5!X1 = 120

Now, there would be only 1 scenario of selecting two red cars. i.e When red colour car takes the 1st place.

So, the spaces can be filled as 
1*4*3*2*1*1 = 24

Thus,
Probability= 24/120 = 1/5

Hope this helps.
Paritosh Rawat

Posted from my mobile device

Dooperman · Answer

6th car will have the same colour as the first car. 
The questions effectively is asking the probability of choosing a red car which is 1/5

nuwaaanda · Answer

I tried looking at this very simply.

The only possibility that we have 2 reds is when the first item we pick is red. For eg. if we have to pick consecutive cars only, and we are picking 6 cars, it will follow the cycle. If we were to pick the blue car first, the cycle would be blue, red, green, yellow, black, blue. We can try these with any colour and it will follow the same cycle, where the colour we start with is the same as the colour we end with.

Hence in the above question, we have to start with red to get 2 reds.

Now, if we have 5 different colours to choose from as our starting colour of picking and red is what we want, then 
No. of desired outcomes: (us picking red) = 1
No. of total outcomes: (Total no. of colors we can pick from) = 5

Hence, probability = 1/5

A certain machine produces toy cars in an infinitely repeating cycle

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A certain machine produces toy cars in an infinitely repeating cycle

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