Two balls are drawn in succession out of a box containing 5 red and 5 white balls. find the probability that at least 1 ball was red, given that the first ball was

Check the tree diagram of the problem:

The first ball can be either Red or Blue, the second ball can either be Red or Blue.

The branches represent all possible scenarios. 

For example, consider the upper branch, the case when both balls are blue:

The first ball is Blue, probability 5/10, the second ball is Blue, probability 4/9 because now there are 4 left blue balls, and 9 balls in total, after we picked the first blue.

The other branches have the same logic.

The question is not completed so we have 2 cases:

"Find the probability that at least 1 ball was red, given that the first ball was red"

here we add the separate probabilities of (R, R) and (R, B)

P(R,R)+P(R,B)=2/9 + 5/18 =  4/18  +5/18= 9/18=0.5

 
"Find the probability that at least 1 ball was red, given that the first ball was blue"

probability is P(B, R)=5/18=0.28

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .

This is too long-standing now get out