First slide

Theorems of probability

Question

There are 20 cards. Ten of these cards have the letter “I” printed on them and the other 10 have the letter “T” printed on them. If three cards are picked up at random and kept in the same order, the probability of making word IIT is

Moderate

A

4/27
B

5/38
C

1/8
D

9/80

Solution

Consider the following events:
A : getting a card with mark I in first draw
B : getting a card with mark I in second draw
C : getting a card with mark T in this draw
Then, the required probability is
$\begin{array}{l} P (A \cap B \cap C) = P (A) P (B / A) P (C / A \cap B) \\ = \frac{10}{20} \times \frac{9}{19} \times \frac{10}{18} = \frac{5}{38} \end{array}$

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