Question

A box contains seven action, six comedies, eight dramas, and five science fiction films. Find the probability of choosing a comedy, putting it back and choosing a drama. I cant figure out really HOW to do this question either.

Answer 1

7 action, 6 comedies, 8 dramas and 5 science fiction. So our sample space or possible outcomes is 7+6+8+5, or 26.

one thing to note is that AND means multiplication.

P(comedy) will be 6/26, favorable outimes over possible outcomes, and then we put it back, because we're putting it back in the box, the sample space is again 26, therefore P(drama) is 8/26, and then we multiply both.

$\bf \stackrel{P(comedy)}{\cfrac{6}{26}}~~\stackrel{\stackrel{AND}{\downarrow }}{\cdot }~~\stackrel{P(drama)}{\cfrac{8}{26}}\implies \cfrac{3}{13}\cdot \cfrac{4}{13}\implies \cfrac{12}{169}~~\approx~~0.071\\\\\\0.071\cdot 100\implies \stackrel{\%}{7.1}$

Answer 2

Answer: The required probability = (6/26)*(8/26) = 0.071