goodie bag probability

Question

at a national event, each goodie bag contained 18 red sweets and x white sweets. The probability that a sweet drawn at random will be white is 3/5.

find the value of x?

Answer 1

You can use a proportion in this case. But it is a little tricky. The probability given to us tells us that there are 3 whites for a total of 5 goodies (red plus white). We want to know how many whites (x) there are when there are a total of x whites plus 18 reds:

Now, cross multiply:

3(18 + x) = 5x

54 + 3x = 5x

54 = 2x

x = 27

So there are 27 whites. Since there are 18 reds, the total is 45 and (27 whites)/(45 total)can be reduced to 3/5

Answer 2

In probability, all scenarios will sum to 1. In this case, we only have 2 scenarios: Drawing a red candy, and drawing a white candy.

P(red) + P(white) = 1

P(white) is given as 3/5, so using the above equation, we can solve for P(red):

P(red) = 1 - 3/5 = 2/5

We also know that there are 18 red candies, so we can find the total number of candies, since P(red) = red/total

2/5 = 18/total

Total = 45 candies.

Now that we know the total number of candies, and we were given the number of red candies, we can solve for the number of white candies:

Total = red + white

45 = 18 + x

x = 27

We can check to make sure that the probability comes out to 3/5:

27 / 45 = 3/5