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You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a 2 and then picking a 2?

Solution

You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a 2 and then picking a 2?

Solution

\frac{1}{169}

Solution steps

Find the probability of picking a 2:

\frac{1}{13}

Find the probability of then picking a 2:

\frac{1}{13}

Since the events are independent, Use the formula

P (X_{1} \land X_{2} \land \dots \land X_{k}) = P (X_{1}) \cdot P (X_{2}) \cdot \dots \cdot P (X_{k})

= \frac{1}{13} \cdot \frac{1}{13}

\frac{1}{13} \cdot \frac{1}{13} = \frac{1}{169}

= \frac{1}{169}

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