What is the probability of picking an ace?

Probability =

What is the probability of picking an ace? 4 / 52 =.077 or 7.7 chances in 100

Every card has the same probability of being picked

What is the probability of getting a 10, J, Q, or K?

(.077) + (.077) + (.077) + (.077) = / 52 =.308

What is the probability of getting a 2 and then after replacing the card getting a 3 ?

(.077) * (.077) =.0059

What is the probability that the two cards you draw will be a black jack?

10 Card = (.077) + (.077) + (.077) + (.077) =.308 Ace after one card is removed = 4/51 =.078 (.308)*(.078) =.024

Practice What is the probability of rolling a “1” using a six sided dice? What is the probability of rolling either a “1” or a “2” with a six sided dice? What is the probability of rolling two “1’s” using two six sided dice?

Practice What is the probability of rolling a “1” using a six sided dice? 1 / 6 =.166 What is the probability of rolling either a “1” or a “2” with a six sided dice? What is the probability of rolling two “1’s” using two six sided dice?

Practice What is the probability of rolling a “1” using a six sided dice? 1 / 6 =.166 What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) =.332 What is the probability of rolling two “1’s” using two six sided dice?

Practice What is the probability of rolling a “1” using a six sided dice? 1 / 6 =.166 What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) =.332 What is the probability of rolling two “1’s” using two six sided dice? (.166)(.166) =.028

Next step Is it possible to apply probabilities to a normal distribution?

Theoretical Normal Curve -3  -2  -1   1  2  3 

Theoretical Normal Curve -3  -2  -1   1  2  3  Z-scores

We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less? -3  -2  -1   1  2  3  Z-scores

We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less. -3  -2  -1   1  2  3  Z-scores

With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is -3  -2  -1   1  2  3  Z-scores

What is the probability of getting a score of 1 or higher? -3  -2  -1   1  2  3  Z-scores

These values are given in Table C on page  -2  -1   1  2  3  Z-scores

To use this table look for the Z score in column A Column B is the area between that score and the mean -3  -2  -1   1  2  3  Z-scores Column B

To use this table look for the Z score in column A Column C is the area beyond the Z score -3  -2  -1   1  2  3  Z-scores Column C

The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score -3  -2  -1   1  2  3  Z-scores Column C Column B

Practice What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? Between mean and z =.56? Beyond z = 2.25? Between the mean and z = -1.45

Practice What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? Between mean and z =.56?.2123 Beyond z = 2.25? Between the mean and z = -1.45

Practice What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? Between mean and z =.56?.2123 Beyond z = 2.25?.0122 Between the mean and z = -1.45

Practice What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? Between mean and z =.56?.2123 Beyond z = 2.25?.0122 Between the mean and z =

Practice What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher?.1056

Note This is using a hypothetical distribution Due to chance, empirical distributions are not always identical to theoretical distributions If you sampled an infinite number of times they would be equal! The theoretical curve represents the “best estimate” of how the events would actually occurThe theoretical curve represents the “best estimate” of how the events would actually occur

Theoretical Distribution

Empirical Distribution based on 52 draws

Theoretical Normal Curve 

Empirical Distribution

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Theoretical Normal Curve  Normality frequently occurs in many situations of psychology, and other sciences