2/25 Probability

Probability is defined as:

• The measure of determining all possible outcomes of an event.

• The measure of how likely an event is to occur.

• The determination of the number of favorable outcomes of an event.

• The determination if an event will occur.

Answer explanation

Probability is the measure of how likely an event is to occur.

The set of all possible outcomes is called

• Likelihood

• Probability

• The sample space

• Ratio

Answer explanation

The set of all possible outcomes is called the sample space.

For equally likely outcomes, the theoretical probability of an event is the ratio of

• The number of favorable events to the total number of outcomes possible.
  
  

• The number of outcomes possible to the number of favorable events.

Answer explanation

For equally like outcomes, the theoretical probability of an event, P(E), is the ratio of the number of favorable outcomes t the total number of outcomes possible.

A letter in the word 'MATH' is randomly selected. What is the probability of selecting a vowel?

• $\frac{1}{4}$

• $\frac{2}{4}$

• $\frac{3}{4}$

• $\frac{4}{4}$

Answer explanation

The favorable outcome would be to select a vowel (a). There are four letters in the word math so there are four possible outcomes (m,a,t,h). Therefore, the probability of selecting a vowel is 1/4.

A jar contains 7 purple marbles and 12 blue marbles. What is the probability that a randomly selected marble is purple?

• $\frac{7}{12}$

• $\frac{12}{7}$

• $\frac{7}{19}$

• $\frac{19}{7}$

Answer explanation

The favorable outcome would be to select a purple marble. There are 7 purple marbles. There are 19 marbles in total (7+12) therefore there are 19 possible outcomes. The probability of choosing a purple marble is 7/19.

The complement of an event is...

• The sample space.

• The probability of multiple events happening.

• The probability of an event happening.

• The probability of an event NOT happening.

Answer explanation

The complement of an event is the probability of an event NOT happening.

A letter in the word 'MATH' is randomly selected. What is the probability that you will NOT select a vowel?

• $\frac{1}{4}$

• $\frac{2}{4}$

• $\frac{3}{4}$

• $\frac{4}{4}$

Answer explanation

The favorable outcome would be to select a vowel (a). There are four letters in the word math so there are four possible outcomes (m,a,t,h). Therefore, the probability of selecting a vowel is 1/4.  This question asks for the complement of that event.  Therefore the complement is 1 - 1/4 or 3/4. 

A compound event is:

• The probability of two or more simple events.

• The probability of a singular event occurring.

Answer explanation

Compound events - the probability of two or more simple events.

An independent event is:

• When the outcome of one even does not affect the outcome of the other event.

• When the outcome of one event does affect the outcome of the other event.

Answer explanation

An independent event is when the outcome of one even does not affect the outcome of the other event. Written as P(A and B) = P(A) * P (B).

A dependent event is:

• When the outcome of one even does not affect the outcome of the other event.

• When the outcome of one event does affect the outcome of the other event.

Answer explanation

A dependent event is when the outcome of one even does affect the outcome of the other event. Written as P(A and B) = P(A) * P (B, after A occured).