# Probability Math Problems

The probability of selecting a blue ball in the first draw is 0.5.What is the probability of drawing a red ball, given that the first ball drawn was blue?An event that doesn’t occur at all is called an impossible event and its probability is 0.

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There are 5 ways to get a sum of 8 when two dice are rolled = .

And there are two ways where the number on the first die is greater than the one on the second given that the sum should equal 8, G = . Now, P(G|sum equals 8) = P(G and sum equals 8)/P(sum equals 8) = (2/36)/(5/36) = 2/5 A bag contains blue and red balls. The probability of selecting a blue and then a red ball is 0.2.

In mathematics too, probability indicates the same – the likelihood of the occurrence of an event.

Examples of events can be : Either an event will occur for sure, or not occur at all.

Probability of drawing a king = 4/52 = 1/13 After drawing one card, the number of cards are 51. Now, the probability of drawing a king and queen consecutively is 1/13 * 4/51 = 4/663 Conditional probability is calculating the probability of an event given that another event has already occured .

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The formula for conditional probability P(A|B), read as P(A given B) is Consider the following example: Example: In a class, 40% of the students study math and science. What is the probability of a student studying science given he/she is already studying math?

Mutually exclusive events are those where the occurrence of one indicates the non-occurrence of the other OR When two events cannot occur at the same time, they are considered mutually exclusive.

Taking the individual probabilities of each number, getting a 2 is 1/6 and so is getting a 5.

Example 2: Consider another example where a pack contains 4 blue, 2 red and 3 black pens.

If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen?

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