Question

a drawer holds 4 red hats and 4 blue hats.what is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?

Answer 1

"We can draw 4 hats out of 8 with replacement in 84 ways

For drawing exactly 3 red hats:

We can draw 3 red hats out of 4 with replacement in 43ways

We can draw 1 blue hat out of 4 in 4 ways

We can draw 3 red hats and 1 blue hat =(43)×4× 4C3 = 45ways

Similarly,

For drawing exactly 3 blue hats:

We can draw 3 blue hats and 1 red hat in (43)× 4× 4C3 = 45 ways

Total probability = 45+4584 = 12

"