A bag contains marbles of five different colours. One marble is chosen at random. The probability of choosing a brown marble is 0.3 . Choosing a brown marble is three times as likely as choosing a purple marble. Choosing a green marble is equally likely as choosing a purple marble. Choosing a red marble is equally likely as choosing a yellow marble. The probability of choosing a marble that is either red or green is
(A) 0.2
(B) 0.25
(C) 0.35
(D) 0.4
(E) 0.55
Solution 1

We begin by assuming that there are 100 marbles in the bag.

The probability of choosing a brown marble is 0.3 , and so the number of brown marbles in the bag must be 30 since $\frac{30}{100}=0.3$.

Choosing a brown marble is three times as likely as choosing a purple marble, and so the number of purple marbles in the bag must be $30 \div 3=10$.

Choosing a green marble is equally likely as choosing a purple marble, and so there must also be 10 green marbles in the bag.

Since there are 30 brown marbles, 10 purple marbles, and 10 green marbles in the bag, then there are $100-30-10-10=50$ marbles in the bag that are either red or yellow.

Choosing a red marble is equally likely as choosing a yellow marble, and so the number of red marbles in the bag must equal the number of yellow marbles in the bag.

Therefore, the number of red marbles in the bag is $50 \div 2=25$.

Of the 100 marbles in the bag, there are $25+10=35$ marbles that are either red or green.

The probability of choosing a marble that is either red or green is $\frac{35}{100}=0.35$.

## Solution 2

The probability of choosing a brown marble is 0.3 .

The probability of choosing a brown marble is three times that of choosing a purple marble, and so the probability of choosing a purple marble is $0.3 \div 3=0.1$.

The probability of choosing a green marble is equal to that of choosing a purple marble, and so the probability of choosing a green marble is also 0.1 .

Let the probability of choosing a red marble be $p$.

The probability of choosing a red marble is equal to that of choosing a yellow marble, and so the probability of choosing a yellow marble is also $p$.

The total of the probabilities of choosing a marble must be 1 .

Therefore, $0.3+0.1+0.1+p+p=1$ or $0.5+2 p=1$ or $2 p=0.5$, and so $p=0.5 \div 2=0.25$.

The probability of choosing a red marble is 0.25 and the probability of choosing a green marble is 0.1 , and so the probability of choosing a marble that is either red or green is $0.25+0.1=0.35$.

ANSWER: (C)