A box contains 15 large marbles and 11 small marbles. Each marble is either green or white. 8 of the large marbles are green, and 5 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.

Step-by-step explanation:

Given: A box contains 15 large marbles and 11 small marbles. Each marble is either green or white. 8 of the large marbles are green, and 5 of the small marbles are white.

To find: probability that a marble randomly selected is small or green

Solution:

Total number of marbles =

Number of small marbles that are white = 5

Also, each marble is either green or white.

So,

Number of small marbles that are green =

Total number of green marbles = Number of large marbles that are green + Number of small marbles that are green

=

Probability = Number of favorable outcomes ÷ Total number of outcomes

Let E denotes the event that a marble selected is small.

Let F denotes the event that a marble selected is green.

P(E) = Number of small marbles ÷ Total number of marbles

       =

P(F) = Number of green marbles ÷ Total number of marbles

      =

P(E∩F) =

Probability that it is small or green = P(E∪F)

= P(E) + P(F) -P(E∩F)

=

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)