Question

14 black balls and 6 white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball?a) 0.3333
b) 0.2381
c) 0.0952
d) 0.2143
e) 0.3111

Answer 1

Answer:

$Probability = 0.30$

Step-by-step explanation:

Given

Represent Black with B and White with W

$B = 14$

$W = 6$

Required

Probability of the second selection being white

This means that: The first selection could be white or black but the second must be white.

This probability would be represented as thus:

$Probability = (P(W)\ and\ P(W))\ or\ (P(B)\ and\ P(W))$

And it is calculated as:

$Probability = (\frac{n(W)}{Total} * \frac{n(W)-1}{Total - 1}) + (\frac{n(B)}{Total} * \frac{n(W)}{Total - 1})$

Notice that, the second selection has total -1 has its denominator. This is so because, the first selection was made without replacement

So, the formula becomes

$Probability = (\frac{6}{20} * \frac{6-1}{20- 1}) + (\frac{14}{20} * \frac{6}{20- 1})$

$Probability = (\frac{6}{20} * \frac{5}{19}) + (\frac{14}{20} * \frac{6}{19})$

$Probability = \frac{30}{380}+ \frac{84}{380}$

$Probability = \frac{30 + 84}{380}$

$Probability = \frac{114}{380}$

$Probability = 0.30$

Answer 2

The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Given :

• 14 black balls and 6 white balls are placed in an urn.
• Two balls are then drawn in succession.

The formula given below can be used in order to determine the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.

$\rm P = \left(\dfrac{n(W)}{Total}\times \dfrac{n(W)-1}{Total-1}\right)+ \left(\dfrac{n(B)}{Total}\times \dfrac{n(W)}{Total-1}\right)$

Now, substitute the values of known terms in the above formula.

$\rm P = \left(\dfrac{6}{20}\times \dfrac{6-1}{20-1}\right)+ \left(\dfrac{14}{20}\times \dfrac{6}{20-1}\right)$

Simplify the above expression.

$\rm P = \dfrac{30}{380}+\dfrac{84}{380}$

$\rm P =\dfrac{114}{380}$

P = 0.33

So, the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.

Therefore, the correct option is a).

For more information, refer to the link given below:

https://brainly.com/question/23044118