Probability

Keywords in Probability

• CHANCE - a possibility of something happening.

• Event - a thing that happens or takes place, especially one of importance.

• RANDOM - made, done, or happening without method or conscious decision.

• PREDICTABLE - An expected result

• Sample Space  - he sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

• Bias -  Bias, prejudice mean a strong inclination of the mind or a preconceived opinion about something or someone. A bias may be favorable or unfavorable: bias in favor of or against an idea.

• Outcome - an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive. All of the possible outcomes of an experiment form the elements of a sample space

The probability vocabulary and scale

• Probabilities go from 0 to 1 as decimals and fractions or from  0% to 100%

• A probability of 1 or 100 % is described as CERTAIN

• A probability of 0 is said to be IMPOSSIBLE 

• A probability of 50 % or 1/2 or 0.5 is described as being EVEN

•  A probability of between 0 and 0.5 or 0 and 1/2 or 0 % and 50 % is described as being UNLIKELY 

• A probability between 0.5 and 1or 1/2 and 1 or 50 % and 100 % is described as being LIKELY 

Types of Probabilities

• Experimental Probability or relative frequency - Experimental probability is probability that is determined on the basis of the results of an experiment repeated many times

• Theoretical Proability - Theoretical probability is probability that is determined on the basis of reasoning.

Multiple Choice

Which of the following can NOT be a probability?

• 0

• 0.5

• 1

• 1.5

Fill in the Blanks

Multiple Choice

When rolling a single die, the events of rolling an even number and rolling a ‘5’ are mutually exclusive.

• True

• False

Multiple Choice

If you roll one die, what is the probability of getting an odd number or a 4?

• 2/3
• 1/3
• 1/2
• 1/6

Multiple Choice

Danny has 20 chocolates. 5 are milk chocolates, 10 are dark chocolates, and 5 are white chocolates. What is the probability of getting a milk chocolate or a dark chocolate?

• 3/4

• 1/2

• 1/15

• 3/10

Compound Event

• made up of 2 or more simple events (such as rolling a die & flipping a coin

• can be independent or dependent

Independent Event

the probability of one event DOES NOT affect the probability of another event ex. the results of flipping a coin does not affect the results of rolling a die

Dependent Event

the probability of one event DOES affect the probability of another event ex pulling a card from a deck of playing cards, not replacing it and then pulling another card

Multiple Choice

A bag has 2 black and 3 red marbles. You reach into the bag, select a marble and do not replace it. What is P(red, then red)?

• 9/25

• 1/9

• 3/10

• 1/72

Multiple Choice

Two cards are drawn from a deck of 52 cards. What is the probability that the first card drawn is a king and the second card drawn is a heart, given that the first card is replaced?

• 2/52
• 1
• 13/52
• 1/52

Multiple Choice

Rachel is having breakfast. She will choose one item from the menu shown for breakfast and one item to drink. What is the probability Rachel will pick to eat cereal but will not pick water to drink? P(cereal, not water) =

• 3/20

• 1/5

• 3/4

• 2/3

Multiple Choice

The tree diagram shows the outcomes of rolling a die and flipping a coin.

What is the probability of rolling a 1 and flipping tails together?

• 1/6

• 1/12

• 1/2

• 0

Multiple Choice

How many total outfit options are represented?

• 12
• 22
• 3

Multiple Choice

Which one is the sample space for flipping 3 coins?

• {H, T}

• {H1, H2, H3, T1, T2, T3}

• {HHH, TTT, HTH, THT, TTH, HHT}

• {HHH, TTT, HTH, THT, TTH, HHT, HTT, THH}

Multiple Choice

Rolling a pair of dice, find P(sum is 7 or 11).

• 50%

• 16%

• 17%

• 22%