Question

A man has 2 sticky-pads, one red and the other green, each with 6 pages, in his drawer. While solving mathematics
problems, he randomly picks one pad without looking, solves one problem and tears off the page. What is the
probability that, after solving 6 problems, the red pad has 2 more pages than the green one?​

Answer 1

Answer:

The required probability is $\frac{1}{12^{6}}$

Step-by-step explanation:

According to the question,

6 problems are solved

=> 6 pages are torn

Let the red sticky pad be represented by R

and the green sticky pad by G

The remaining pages can be 0R+6G or 1R+5G or 2R+4G or 3R+3G or 4R+2G or 5R+1G or 6R+0G

It is given that after solving 6 problems, red pad has 2 more pages than the green one

=> R = 2 + G

We now substitute the values from above, that satisfies the condition.

Therefore, R = 4 and G = 2

Therefore, 2R pages and 4G pages were used

=> The probability is: $\frac{1}{12}$ *   $\frac{1}{12}$ *   $\frac{1}{12}$ *   $\frac{1}{12}$ *   $\frac{1}{12}$ *   $\frac{1}{12}$ = ( $\frac{1}{12}$ )⁶ =  $\frac{1}{12^{6}}$

Therefore, the required probability is $\frac{1}{12^{6}}$

Answer 2

The probability that, after solving 6 problems, the red pad has 2 more pages than the green one is 75/308  or about  0.2435

Given:

• A man has 2 sticky-pads, one red and the other green, each with 6 pages
• He randomly picks one pad without looking, solves one problem and tears off the page

To Find:

• The probability that, after solving 6 problems, the red pad has 2 more pages than the green one

Solution:

• Probability of an event  = n(E)/n(S)  
• n(E) = number of possible outcome of event
• n(S) = number of possible sample space outcome

Step 1:

the red pad has 2 more pages than the green one

Red has 4 pages left and Green has 2 pages left

Red Pages Tear = 2

Green Pages Tear = 4

Step 2:

Number of ways 6 pages can be tear out of 12 are ¹²C₆

Step 3:

Number of ways 2 Red pages out of 6 and 4 White pages out of 6 can be tear in ⁶C₂.⁶C₄  ways

Step 4:

Find Probability

⁶C₂.⁶C₄ / ¹²C₆

= 15*15/924

= 75/308

≈ 0.2435

The probability that, after solving 6 problems, the red pad has 2 more pages than the green one is 75/308  or about  0.2435