3.5 Tree and Venn Diagrams

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

a. List the 24 BR outcomes: B1R1, B1R2, B1R3, . . .

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

b. Calculate P(RR).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

c. Calculate P(RB OR BR).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

d. Using the tree diagram, calculate P(R on 1st draw AND B on 2nd draw).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

f. Using the tree diagram, calculate P(BB).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

g. Using the tree diagram, calculate P(B on the 2nd draw GIVEN R on the first draw).

Calculate the following probabilities using the tree diagram:

a. P(RR) = ________

Calculate the following probabilities using the tree diagram:

b. Fill in the blanks.

P(RB OR BR) = $\left(\frac{3}{11}\right) \left(\frac{8}{10}\right) \textrm{ } + \textrm{ }(________)(________)\textrm{ } = \textrm{ } \frac{48}{110}$

Calculate the following probabilities using the tree diagram:

c. Because this is a conditional probability, we restrict the sample space to consider only those outcomes that have a blue marble in the first draw. Look at the second level of the tree to see that P(R on 2nd|B on 1st) = $\frac{3}{10}$

Calculate the following probabilities using the tree diagram:

d. Fill in the blanks.

P(R on 1st AND B on 2nd) = P(RB) = (________)(________) = $\frac{24}{110}$

Calculate the following probabilities using the tree diagram:

e. Find P(BB).

Calculate the following probabilities using the tree diagram:

f. Find P(B on 2nd|R on 1st).

Suppose there are four red balls and three yellow balls in a box. Three balls are drawn from the box without replacement. What is the probability that one ball of each coloring is selected?

Find P(blue bead).

1. $\frac{15}{36}$
2. $\frac{10}{36}$
3. $\frac{10}{12}$
4. $\frac{6}{36}$

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) who are female is 48.60. Of the females, 5.03 percent are age 19 and under; 81.36 percent are age 20–64; 13.61 percent are age 65 or over. Of the licensed U.S. male drivers, 5.04 percent are age 19 and under; 81.43 percent are age 20–64; 13.53 percent are age 65 or over.

Comple…

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) who are female is 48.60. Of the females, 5.03 percent are age 19 and under; 81.36 percent are age 20–64; 13.61 percent are age 65 or over. Of the licensed U.S. male drivers, 5.04 percent are age 19 and under; 81.43 percent are age 20–64; 13.53 percent are age 65 or over.

Approx…