(a) In a game, a fair die is rolled once and two unbiased coins are tossed at once. What is the probability of obtaining 3 and a tail?
(b) A box contains 10 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting:
(i) a red, then a black marble ; (ii) two black marbles.
Explanation
(a) P(obtaining a 3 from a die) = (frac{1}{6})
P(obtaining a tail in 2 coins tossed at once) = (frac{1}{2}).
(therefore) P(obtaining 3 and a tail = (frac{1}{6} times frac{1}{2} = frac{1}{12})
(b) No of black marbles = n(B) = 7
No of red marbles = n(R) = 3
Total marble = 10
(i) P(red then black) = P(1st red, then black) or P(1st black, then red)
= (frac{3}{10} times frac{7}{9} + frac{7}{10} times frac{3}{9})
= (frac{7}{15})
(ii) Prob (two blacks) = (frac{7}{10} times frac{6}{9} = frac{7}{15})