Question

A box contains 4 red pens and 5 black pens. Find the probability of drawing 3 black pens one by one (i) with replacement (ii) without replacement

Answer 1

with replacement it is 5/9
without replacement :
first pen 5/9
second pen 4/8 = 1/2
third pen 3/7

Answer 2

Answer:  The required probabilities are

(i) 17.15%

(ii) 11.90%.

Step-by-step explanation:  Given that a box  contains 4 red pens and 5 black pens.

We are to find the probability of drawing 3 black pen one by one

(i) with replacement

(ii) without replacement.

We have

Total number of pen in the box = 4 + 5 = 9.

(i) The probability of drawing 3 pen one by one with replacement is given by

$p_1=\dfrac{5}{9}\times \dfrac{5}{9}\times\dfrac{5}{9}=\dfrac{125}{729}\times100\%=17.15\%.$

(ii) The probability of drawing 3 pen one by one without replacement is given by

$p_2=\dfrac{5}{9}\times\dfrac{4}{8}\times\dfrac{3}{7}=\dfrac{5}{42}\times100\%=11.90\%.$

Thus, the required probabilities are

(i) 17.15%

(ii) 11.90%.