1. 1. The father determines the gender of the child True or False?

2. 2. Individuals can transmit characteristics to their offspring which they themselves do not show. True or False?

3. 3. Identical twins are always of the same gender. True or False?

4. Probability

5. What is a PROBABILITY? - Probability is the chance that some event will happen - It is the ratio of the number of ways a certain event can occur to the number of possible outcomes Probability of Simple Events

6. What is a PROBABILITY? number of favorable outcomes number of possible outcomes number of possible outcomes Examples that use Probability : (1) Dice, (2) Spinners, (3) Coins, (4) Deck of Cards, (5) Evens/Odds, (6) Alphabet, etc. Probability of Simple Events P(event) =

7. What is a PROBABILITY? What is a PROBABILITY? 0% 25% 50% 75% 100% 0% 25% 50% 75% 100% 0¼ or.25 ½ 0r.5 ¾ or.75 1 0¼ or.25 ½ 0r.5 ¾ or.75 1 Impossible Not Very Equally Likely Somewhat Certain Impossible Not Very Equally Likely Somewhat Certain Likely Likely Likely Likely Probability of Simple Events

8. Example 1: Roll a dice. What is the probability of rolling a 4? # favorable outcomes # favorable outcomes # possible outcomes # possible outcomes 1 1 6 6 The probability of rolling a 4 is 1 out of 6 Probability of Simple Events P(event) = P(rolling a 4) =

9. Example 2: Roll a dice. What is the probability of rolling an even number? # favorable outcomes # favorable outcomes # possible outcomes # possible outcomes 3 1 3 1 6 2 6 2 The probability of rolling an even number is 3 out of 6 or.5 or 50% Probability of Simple Events P(event) = P(even #) = =

10. Example 4: Flip a coin. What is the probability of flipping a tail? # favorable outcomes # favorable outcomes # possible outcomes # possible outcomes 1 1 1 1 2 2 2 2 The probability of spinning green is 1 out of 2 or.5 or 50% Probability of Simple Events P(event) = P(tail) = =

11. Example: If you put all the alphabet letters into a bag what is the probability you would pick out a vowel on the first try?

12. Real World Example: Best Buy is having an IPOD giveaway. They put all the IPOD Shuffles in a bag. Customers may choose an IPOD without looking at the color. Inside the bag are 4 orange, 5 blue, 6 green, and 5 pink IPODS. If Maria chooses one IPOD at random, what is the probability she will choose an orange IPOD? Probability of Simple Events P(orange) = 4 / 20 = 2 / 10 = 1 / 5 or 20%

13. Multiplication Rule for Independent Events Two events A and B are independent if knowing that one event has occurred does not change the probability that the other will occur. Two events A and B are independent if knowing that one event has occurred does not change the probability that the other will occur. multiplication rule for independent events: multiplication rule for independent events: P(A and B) = P(A) * P(B) P(A and B) = P(A) * P(B) Key word is AND

14. Examples Flip a coin once and get ‘heads’. Does this result change the probability of rolling a heads again on the second roll? Flip a coin once and get ‘heads’. Does this result change the probability of rolling a heads again on the second roll? Event 1: Get a heads on first flip. Event 2: Get a heads on second flip. The probability of event #2 is NOT affected by whatever happened on event #1. Therefore, these are independent events Event 1: Get a heads on first flip. Event 2: Get a heads on second flip. The probability of event #2 is NOT affected by whatever happened on event #1. Therefore, these are independent events You buy a lottery ticket and win. Then you win again the next week. Does this change the likelihood of winning on the third week since you are “on a roll”? You buy a lottery ticket and win. Then you win again the next week. Does this change the likelihood of winning on the third week since you are “on a roll”? Event 1: Win the first week. Event 2: Win the second week. Event 3: Win the third week. However, winning the first two weeks in no way affects the likelihood of winning the 3 rd week. In other words, these events are all independent Event 1: Win the first week. Event 2: Win the second week. Event 3: Win the third week. However, winning the first two weeks in no way affects the likelihood of winning the 3 rd week. In other words, these events are all independent

15. Example George wants to get dressed for school. He finds a pair of blue jeans. He has four different color shirts to wear and two different color jackets. How many possible outfits can he dress in? Example A store sells fruit shakes. They have 3 different size cups to use: small, medium, and large. The choice of fruit are banana, orange, pineapple, strawberry, and peach. They can also add whip cream of no whip cream. How many possible combinations of fruit drinks are there?

16. Example: What is the probability of getting a tails on two consecutive coin tosses? We are asking the probability of getting a tails on the first coin toss and on the second coin toss. P(first = Tail and second = Tail) P(first = Tail and second = Tail) = P(first Tail) * P(second Tail) = 0.5 * 0.5 = 0.25

17. A couple intends to have three children. What is the likelihood that they will have only boys? A couple intends to have three children. What is the likelihood that they will have only boys? Answer: After a little bit of thought, you realize that you are being asked P(first child is a boy) AND P(2 nd child is a boy) AND P(3 rd child is a boy). ‘So we may therefore use the multiplication rule: Answer: After a little bit of thought, you realize that you are being asked P(first child is a boy) AND P(2 nd child is a boy) AND P(3 rd child is a boy). ‘So we may therefore use the multiplication rule: P(BBB) = P(B)* P(B)* P(B) = (1/2)*(1/2)*(1/2) = 1/8 P(BBB) = P(B)* P(B)* P(B) = (1/2)*(1/2)*(1/2) = 1/8