# Discrete probability

1. Suppose you randomly draw two marbles, without replacement from a bag, containing six green, four red and three black marbles.

a) Determine the probability that both marbles are red.

b) Determine the probability that you pick at least one green marble.

2. What is the probability of at least two people in a class of 30 students having the same birthday? Assume that no one in the class was born on February 29th.

3. A club with eight members from Grade 11 and five members from Grade 12 is electing a president, vice-president and secretary. What is the probability (as a percentage to one decimal place) that Grade 12 students will be elected for all three positions, assuming that all club members have an equal chance of being elected?

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#### Solution Preview

1.

a) There are 13 marbles in the bag (6+4+3). The probability P(both are red) that both marbles are red is P(the first one is red and the second one is red)=P(the first one is red) x P(the second one is red given that the first one is red).

There are 4 red marbles out of 13. The probability that the first marble is red is 4/13. Now, the probability that the second one is red given that one red was taken out of the bag is 3/12 = 1/4. So, the probability that both marbles are red is 4/13 ...

#### Solution Summary

Several examples of calculating the discrete probability of an event, such as picking at least one green marble when drawing two marbles at random from a bag containing marbles of different colors, or the probability of two students from a class having the same birhday are calculated with detailed explanations.