Practicing Success
A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade, the chance that he will fail in the first two draws is |
$\frac{1}{16}$ $\frac{9}{16}$ $\frac{9}{64}$ $\frac{1}{64}$ |
$\frac{9}{16}$ |
Let $A_i$ be the event that the person ails in ith draw. Then, $P(A_i)= 1 -\frac{13}{52}=\frac{3}{4}, i = 1, 2, 3, .....$ ∴ Required probability $= P(A_1 ∩ A_2)= P(A_1)P(A_2)$ ⇒ Required probability $=\frac{3}{4}× \frac{3}{4}=\frac{9}{16}$ |