Question

Match the following items.

Answer 1

P( two white) = 18/40 * 17/39 = 51/260
P( black then red) = 12/40 * 10/39 = 1/13
P( two black) = 12/40 * 11/39 = 11/130
P( white then black) = 18/40 * 12/39 = 9/65

Answer 2

Answer:

1) Probability of drawing a white, then a black marble? = 0.13

2) Probability   of drawing two black marbles =0.08

3) Probability   of drawing two white marbles = 0.19  

4) Probability   of drawing a black, then a red marble = 0.07    

Step-by-step explanation:

Given : A jar contains a mixture of 12 black marbles, 10 red marbles, and 18 white marbles, all the same size. If two marbles are drawn from the jar without being replaced.

Solution :

Total number of marbles in a jar = 12+10+18=40

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}$

1) To find  what would the probability of drawing a white, then a black marble?

probability of getting a white marble = $\frac{18}{40}=\frac{9}{20}$

Without replacement, total number is 40-1=39

probability of getting a black marble = $\frac{12}{39}=\frac{4}{13}$

Probability of drawing a white, then a black marble is

$P=\frac{9}{20}\times \frac{4}{13}= \frac{36}{260}=0.13$

2) To find  what would the probability of drawing two black marbles?  

probability of getting one black marble = $\frac{12}{40}=\frac{3}{10}$

Without replacement, total number is 40-1=39

probability of getting second black marble = $\frac{11}{39}$

Probability of drawing two black marbles is

$P=\frac{3}{10}\times \frac{11}{39}= \frac{33}{390}=0.08$

3) To find what would the probability of drawing two white marbles?  

probability of getting one white marble = $\frac{18}{40}=\frac{9}{20}$

Without replacement, total number is 40-1=39

probability of getting second white marble = $\frac{17}{39}$

Probability of drawing two white marbles is

$P=\frac{9}{20}\times \frac{17}{39}= \frac{153}{780}=0.19$

4) To find what would the probability of drawing a black, then a red marble?  

probability of getting a black marble = $\frac{12}{40}=\frac{3}{10}$

Without replacement, total number is 40-1=39

probability of getting a red marble = $\frac{10}{39}$

Probability of drawing a white, then a black marble is

$P=\frac{3}{10}\times \frac{10}{39}= \frac{30}{390}=0.07$