Question

A bag contains 3 pink gumballs, 4 red gumballs, and 2 green gumballs. Find the probability that a red gumball is drawn if there are 5 drawings that occur and the gumballs are replaced after each draw. Round your answer to two decimal places.

Answer 1

Answer:

0.99

Step-by-step explanation:

Given,

Pink gumballs = 3,

Red gumballs = 4,

Green gumballs = 2,

So, total gumballs = 3 + 4 + 2 = 9,

Thus, total ways of selecting 5 gumball = $^9C_5$

$=\frac{9!}{5!4!}$

$=\frac{9\times 8\times 7\times 6}{24}$

$=9\times 2\times 7$

$=126$

Also, the total ways of selecting no red gumballs = $^4C_0\times ^5C_5$

= 1 × 1

= 1

So, the probability of no red gumballs in 5 drawn

$=\frac{1}{126}$

Hence, the probability that a red gumball is drawn if there are 5 drawings

= 1 - probability of no red gumballs

$=1-\frac{1}{126}$

$=\frac{125}{126}$

≈ 0.99

Answer 2

Answer:

probability of drawn red balls 0.99

Step-by-step explanation:

Given data: 3 pink ball

4 red gumballs

2 green gumballs

total number of drawing is 5

probability of drawn red balls is given as

P = 1 - Probability of no red ball drawn

  $= 1 - \frac{^4C_0 \times ^5C_5}{ ^9C_5}$

  $= 1 - \frac{1}{126}$

$= \frac{125}{126}$

= 0.99