DOUBLE EVENT PROBABILITY

Introduction

This lesson will deal with mutually exclusive event probability (events that do not effect the outcome of each other). We will determine the probability that two events will have the same specific occurrence (i.e. when two dice are thrown, both land with a "four" showing), the probability that out of the two events only one will have a specific occurrence (i.e. only one die lands with a "four" showing), and the probability that out of the two events neither will have the specific occurrence (i.e. neither die lands with a "four" showing).

* The probability that two mutually exclusive events will have the same specific occurrence is the product of their probabilities.

For example, the probability when two dice are thrown that they both will be a "four" is found as follows:

=

=.

* The probability neither of two mutually exclusive events will have a specific occurrence is the product of the probabilities for each not having the occurrence.

For example, the probability when two dice are thrown that neither will display a "four" is found as follows:

.

* The probability that two mutually exclusive events will have different occurrences is twice the product of the probability one will have the occurrence times the probability the other will not have the occurrence.

For example, the probability when two dice are thrown that only one will be a "four" is found as follows:

.

The reason that we need to multiply by two is because we must account for the first die showing a four with the second not showing a four, and also the first die not showing a four when the second die does show the four.

* The sum of all the probabilities of an event occurring equals one. Notice that the three calculations above have a sum of one. The three calculations are all the possible ways a "four" could occur on two dice. That is:

+ + one

.

Exercises: Find the following related to two event probabilities:

1. What is the probability that when you roll 2 dice they will both land showing a:

a. two? b. six?

2. What is the probability that when you roll 2 dice one will show a two and the other will show a six?

3. What is the probability that when you roll 2 dice neither will show a two or a six?

4. What is the probability that when you roll 2 dice, the first will show a three, and the second will show:

a. a three b. a three or a four

c. a two, three, or four d. a number other than three

5. There are six socks in a drawer (a red, a white and a blue pair). Without looking, what is the probability that when you reach in and pull two socks out they will be:

a. both red b. one red and one blue

c. one white and one red d. one blue and the other pink

e. one red and the other of f. one red or blue, and the other

any color a red or blue

g. no white socks *h. a matching pair

6. A baby can inherit one of 2 alleles per gene from both its mother and father. Suppose the mother's alleles are represented by "D" and "d", and the father's genes are also represented by "D" and "d". What is the probability that when the baby inherits one "letter" (allele) from each parent, its genetic make-up will be:

a. DD b. dd

c. a combination of D and d d. not DD e. not a combination of D and d f. will be the same two letters

g. not the same letter