Question

A box contains 5 yellow toys and 4 red toys. Two toys are selected with replacement.

- Draw a tree diagram showing all outcomes and probabilities

-Find the probability that:
A. Two toys of the same colour will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked

-if there was no replacement, find the probability that:
A. Two toys of the same colours will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked

Answer 1

Kindly check explanation

Explanation:

Given the following :

Yellow (Y) toys = 5

Red (R) toys = 4

Total toys = yellow + red = (5 +4) = 9

WITH REPLACEMENT :

Probability that two toys of same color will be picked.

From the tree diagram.

Two toys of the same color

a.)P(Y, Y) + P(R, R) = (25/81) + (16 / 81) = 41/81

b) toys of different color :

P(Y, R) + P(R, Y) = (20/81) + (20/81) = 40/81

c.) A red toy will be picked first :

P(R, Y) = 20/81

d.) Atleast one red toy will be picked

P(Y, R) + P(R, Y) + P(R, R)

20 /81 + 20/81 + 16/81 = 56/81

2) WITHOUT REPLACEMENT :

a.)P(Y, Y)+P(R, R) = (20/72) + (12/72) = 32/72 = 4/9

b) P(Y, R)+P(R, Y) = (20/72)+(20/72)= 40/72 = 5/9

c) p(R, Y) = 12/72 = 1/6

d) P(Y, R) + P(R, Y) + P(R, R) = 20/72 + 20/72 + 12/72 = 52/72 = 13/ 18