Question

cynara has a bag of red, blue, and black pens. She randomly selects a pen, records the color, and puts it back in the bag, She does this a total of 30 times and selects 6 red pens, 10 blue pens, and 14 black pens. Based on this information, what is the probability that Cynara will select a blue pen, return it to the bag, and then select a red pen?

Answer 1

Divide the number of times she picked a color by the total times she picked a pen:

Red = 6/30 reduces to 1/5

Blue = 10/30 reduces to 1/3

Black = 14/30 reduces to 7/15

The probability of picking a blue pen , then a red pen is found by multiplying the two possibilities together:

1/3 x 1/5 = 1/15

There is a 1/15 probability.

Answer 2

The probability that Cynara will select a blue pen, return it to the bag, and then select a red pen is $\frac{1}{15}$.

Given that,

• She randomly selects a pen, records the color, and puts it back in the bag,
• She does this a total of 30 times and selects 6 red pens, 10 blue pens, and 14 black pens.

Based on the above information, the calculation is as follows:

Here we have to divide the no of times from the total times she picked the pen.

So,  

Red = $6\div 30$ reduces to $1\div 5$

Blue = $10\div 30$ reduces to $1\div 3$

Black = $14\div 30$reduces to $7\div 15$

Now

$= 1\div 3 \times 1\div 5 \\\\= 1\div 15$

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