The tree diagram represents an experiment consisting of two trials.
5
6 3
5
B
P(A and D) = [?]

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.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.