There is a bag with only red marbles and blue marbles. The probability of randomly choosing a blue marble is 2/9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

49 red marbles

Step-by-step explanation:

There is a bag with only red marbles and blue marbles.

We are told in the question that:

The probability of randomly choosing a blue marble is 2/9 . There are 63 marbles in total in the bag

Hence: since

P(Blue marbles) = 2/9

Hence,

The number of blue marbles = 63 ÷ 9

= 7

Hence:

2 × 7/9 × 7 = 14/63

Hence, the number of blue marbles = 14 blue marbles

The number of red marbles bus calculated as:

63 - 14 blue marbles

= 49 red marbles

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)