A jar contains 2 red marbles numbered 1 to 2 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given

Question

(c) The marble is red or odd-numbered
Your answer is :

(d) The marble is blue or even-numbered
Your answer is :

Answer 1

Let's look at c first then you should be able to do d on your own.

 

Let's say P(R) is probability of red and P(O) is probability of odd.

 

The formula we need is:

 

P(R or O) = P(R) + P(O) - P(R and O)

 

For the first part, the probability of getting a red marble, we have 12 total marbles and 2 are red. So the chance of getting a red one is 2/12 or 1/6

 

The second probability is getting an odd number. We have 1 odd red one and 5 odd blue ones, so 6 total. The chance of getting an odd one is 6/12 or 1/2

 

The last probability we need is the chance of getting a red AND odd one. There is only 1 red marble with an odd number, so the chance is 1/12

 

Now we use our formula and fill in the numbers:

 

P(R or O) = P(R) + P(O) - P(R and O)

 

P(R or O) = 1/6 + 1/2 - 1/12

= 2/12 + 6/12 - 1/12

= 7/12

 

So the chance of getting a red or an odd numbered marble is 7/12

 

Part d is done in the same manner, just use the probability of blue or even instead of red or odd