Section P.1 – Fundamental Principles of Probability

number of winners compute second Probability = compute first Group 1 – What are you doing? If two cards are chosen from a standard deck, find the probability that exactly one card is black.

If five die are rolled, find the probability that the sum of the faces showing is at least three. If five die are rolled, find the probability that the sum of the faces showing is at least 100. Group 2 – What are you doing? If a pair of dice is rolled, find the probability that the sum of the faces showing greater than 3.

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If a pair of dice is rolled, find the probability that the sum of the faces showing greater than 3.

Ratios reduce like fractions Group 3 – What are you doing? If three numbers are drawn from a bag containing the numbers 1-30 (inclusive), find the ODDS all three numbers drawn are odd.

State the odds of an event occurring given the probability of the event.

Group 4 – What are you doing? Tim is playing a game at the carnival in which he tosses two coins. If both coins land heads, he wins $2. If both coins land tails he wins $1. What can Tim expect to win?

Group 5 – What are you doing? Katie is playing a different game at the carnival. She pays $1 for a chance to roll three die. If all three numbers showing are even, she wins $2. If all three numbers showing are odd, she wins $3. If Katie plays the game 10 times, how much should she expect to win or lose?

Group 6 – What are you doing? Eamonn is playing a different game at the carnival. In this games, five numbers are pulled from a bag. If the product of those five numbers is even, he wins $5. Eamonn pays $2 to play this game. Find the probability Eamonn wins the game. Find the odds of Eamonn LOSING this game. Find the expectation in this game. How much can Eamonn expect to win or lose if he plays the game five times?

Repetition NOT allowed Independent Dependent Roll a Die Twice Draw two cards with replacement Draw two cards without replacement Choose two letters Repetition allowed Choose two letters Repetition NOT allowed Consistent Denominator For each individual trial Denominator Reduces For each individual trial

Two die are rolled. Find the probability that neither is a 5. Independent vs. Dependent Events Rule of Thumb Do the event twice On the second time of event, check number of possibilities If the same…..independent…separate fractions If different……dependent…...single fraction…. most likely combinations to be used

From a standard deck of cards, five are drawn. What are the odds of each selection? a. five aces Zero…..there are only four aces in a deck. b. five face cards ODDS 792:2598168 33:108257

When Jon shoots a basketball, the probability that he will make a basket is 0.4. When Kayla shoots, the probability of a basket is 0.7. What is the probability that at least one basket is made if Jon and Kayla take one shot each? P(at least one) = 1 – P(none) P(at least one basket) = 1 – P(no baskets) P(Carlos missing) = 0.6 P(Brad missing) = 0.3

According to the weather reports, the probability of snow on a certain day is 0.7 in Frankfort and 0.5 in Champaign. Find the probability of each: a. It will snow in Frankfort, but not in Champaign. b. It will snow in both cities. c. It will snow in neither city. d. It will snow in at least one of the cities.

number of winners compute second Probability = compute first Independent Events Dependent Events Consistent Denominator for each individual trial Denominator Reduces for each individual trial (cominbations required)