The tree diagram represents an
experiment consisting of two trials.

answer is in photo.

Green one is main answer and blue one is formula

Explanation:

Highlight the path that starts with A and then leads to D

Multiply the values highlighted to get 0.5*0.6 = 0.3

Effectively we've computed the following

P(A and D) = P(A)*P(D given A)

P(A and D) = 0.5*0.6

P(A and D) = 0.3

The notation "D given A" indicates we know event A has happened. We cannot simply say P(D) because there is another event D that happens on the lower branch B; so instead we say P(D given A). You can replace the word "given" with a vertical bar to write P(D | A), though in my opinion the vertical bar could be easily mistaken for the uppercase letter i, a lowercase letter L, or the numeric digit "one". I find its easier to describe what is going on rather than use the vertical bar notation.

answer is in photo.

Green one is main answer and blue one is formula

Explanation:

Highlight the path that starts with A and then leads to D

Multiply the values highlighted to get 0.5*0.6 = 0.3

Effectively we've computed the following

P(A and D) = P(A)*P(D given A)

P(A and D) = 0.5*0.6

P(A and D) = 0.3

The notation "D given A" indicates we know event A has happened. We cannot simply say P(D) because there is another event D that happens on the lower branch B; so instead we say P(D given A). You can replace the word "given" with a vertical bar to write P(D | A), though in my opinion the vertical bar could be easily mistaken for the uppercase letter i, a lowercase letter L, or the numeric digit "one". I find its easier to describe what is going on rather than use the vertical bar notation.

P(A) = 0.5

Step-by-step explanation:

Look from the tree root (left) and find A.  

When you reach the first branch that shows A, the probability is on it's left, so

P(A) = 0.5

The probability defined as P(A and C) is the probability of P(A) × P(B) = (0.6 × 0.3) = 0.18

The probability of A ; P(A) from the tree diagram is 0.6

The probability of B ; P(B) from the tree diagram is 0.3

The probability, P(A and B) equals ;

P(A) × P(B) = 0.6 × 0.3 = 0.18

Therefore, probability of A and B is 0.18

.26

Step-by-step explanation:

P(C) = .6*.3   + .4 *.2

       = .18+.08

      = .26

P(D) = 0.65

Step-by-step explanation:

Follow the segments that lead to D.

First, it's 0.5 to A and then 0.6 to D.

Then, it's 0.5 to B and 0.7 to D.

P(D) = 0.5 * 0.6 + 0.5 * 0.7 = 0.3 + 0.35 = 0.65

P(D) = 0.65

See explanation

Explanation:

1. an organizing tool used to find the sample space for compound events = Tree diagram

A tree diagram is used to show the probability space.

2. a game in which each participant has the same probability of winning = Fair game

3. an event consisting of two or more events that can happen at the same time or one after the other= Compound event

4. the set of all possible outcomes for an experiment = Sample space

A sample space consists of all the possible outcomes that can be gotten in a probability.

5. principle that states the number of outcomes for a compound event is found by multiplying the total number of outcomes for each event together = Counting Principle

Counting Principle is used to know the number of outcomes that one can get in a probability problem. This is done by multiplying the events together in order to get the outcomes.

See explanation

Explanation:

1. an organizing tool used to find the sample space for compound events = Tree diagram

A tree diagram is used to show the probability space.

2. a game in which each participant has the same probability of winning = Fair game

3. an event consisting of two or more events that can happen at the same time or one after the other= Compound event

4. the set of all possible outcomes for an experiment = Sample space

A sample space consists of all the possible outcomes that can be gotten in a probability.

5. principle that states the number of outcomes for a compound event is found by multiplying the total number of outcomes for each event together = Counting Principle

Counting Principle is used to know the number of outcomes that one can get in a probability problem. This is done by multiplying the events together in order to get the outcomes.