There are 5 red pens and 10 black pens in a cup. if a person randomly selects 3 of them, what is the probability that they're all the same color?

a. 0.286
b. 0.18
c. 0.264
d. 0.379

option a)

0.286

Step-by-step explanation:

Given that,

number of red pens in cup = 5

number of black pens in cup = 10

number of pen randomly selected = 3

There are 5 red pens and 10 black pens. So there are 5 + 10 = 15 pens in all.

probability of having all red pens = (5/15 x 4/14 x 3/13)

                                                       = 2/91

probability of having all black pens = (10/15 x 9/14 x 8/13)

                                                           = 24/91

probability that all pen are of same colour = 24/91 + 2/91

                                                                      =  2/7

                                                                      ≈ 0.286

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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