I understand the basics of probability but I need help with the following?

1. What is the probability that when 2 numbered cubes are thrown that at least 1 will land with the number 6 up? Why is the answer 11/36?

2. What is the probability that when 3 spinners with the numbers 1-3 are spun that at least 2 will land on a prime number? Why is the answer 20/27?

Thanks in advance!

1. What is the probability that when 2 numbered cubes are thrown that at least 1 will land with the number 6 up? Why is the answer 11/36?


1. The probability of throwing a 6 with a single die is 1/6. The probability of throwing a six with a second die is also 1/6. However, it's a bit more difficult to figure out the probability that at least one will be a six.

The probability of not throwing a six is 5/6.

The probability of not throwing a six with two dice is \frac 56 \,\times\, \frac 56 = \frac {25}{36}

The probability, therefore, that you throw at least one six with two dice is 1-\frac {25}{36}=\frac {11}{36}

In a bag are only red and white marbles. The probability of choosign a red marble is 3/5. The probability of choosing two red marbles without replacement is 3/10. How many marbles are in the bag?