Aball is drawn at random from a box containing 12 red,18
white,19 blue and 15 orange balls. find the probability that(1) it
is red or blue, (2) white, blue or orange, (3) neither white nor
orange.

For a: The probability of getting a red or blue ball is 0.48

For b: The probability of getting a white, blue or orange ball is 0.81

For c: The probability of getting neither white or orange ball is 0.48

Step-by-step explanation:

Probability is defined as the extent to which an event is likely to occurs. It is measured by the ratio of the favorable outcomes to the total number of possible outcomes.

    .......(1)

We are given:

Number of red balls in a box = 12

Number of white balls in a box = 18

Number of blue balls in a box = 19

Number of orange balls in a box = 15

Total balls in a box = [12 + 18 + 19 + 15] = 64

Number of favorable outcomes (ball must be red or blue) = [12 + 19] = 31

Total number of outcomes = 64

Putting values in equation 1, we get:

Number of favorable outcomes (ball must be white or blue or orange) = [18 + 19 + 15] = 52

Total number of outcomes = 64

Putting values in equation 1, we get:

Number of favorable outcomes (ball must be white or orange) = [18 + 15] = 33

Total number of outcomes = 64

Putting values in equation 1, we get:

Probability of getting a ball which is neither white or orange = [1 - (Probability of getting a white or orange ball)] = [1 - 0.52] = 0.48

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)