Question

a jar contains red and blue marbles the probability that a randomly-selected marble is red is 1/4 if 27 of the marbles are blue how many marbles are in the jar

Answer 1

Hi!
So if you know the probability of choosing a red marble in that given jar is 1/4, you can then figure out what the probability of not choosing a red marble, or choosing a blue marble, is. That probability would be called the complement of 1/4, and what would be added to it to make 1. In this case, it would be 3/4.
Since 27 of the marbles are blue, and the chance of drawing a blue marble is 3/4, we can then say 27 = 3/4 of the jar. Now the easier way is to find what 1/4 then equals and add it up. Since 1/4 is 1/3 of 3/4, we can see what 1/3 of 27 is to find what 1/4 of the marbles in the jar is.
1/3 • 27 = 9.
So if we add 9 and 27 together, that's the total number of marbles in the jar. 27 + 9 = 36.
There are 36 marbles in the jar.