Question

Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads. For the coin, $P\left(H\right)=\frac{2}{3}$and $P\left(T\right)=\frac{1}{3}$where H is heads and T is tails.

Find P(tossing a Head on the coin AND a Red bead)

a. $\frac{2}{3}$

b. $\frac{5}{15}$

c. $\frac{6}{36}$

d. $\frac{5}{36}$

Short answer

c.$\frac{6}{36}$

Step-by-step solution

Given information

This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads.

Explanation 

From the given information, the Probability of tossing a Head on the coin AND a Red bead:

$$\begin{gathered} P(tos\sin gaHeadANDaRedbead)=P(tos\sin gaHead).P(aRedbead) \\ P(tos\sin gaHeadANDaRedbead)=\frac{2}{3}\times \frac{3}{12}=\frac{6}{36} \end{gathered}$$