Question

You pick a card at random without putting the 1st card back you pick a second card at random what is the probability of picking a 7 then picking a number greater than 7cards: 7,8,9

Answer 1

The probability of 2 consecutive events is the product of the probability of the single events.

The probability of an single event A is the quotient of the number of favorable outcomes to A and the total number of outcomes.

First, let's calculate the probability of picking a 7.

Favorable outcome: 7

Number of favorable outcomes: 1

Total possible outcomes: 7, 8, 9

Number of total outcomes: 3

Then, the probability is of picking a 7:

$P(picking\text{ }a\text{ }7)=\frac{1}{3}$

Second let's calculate the probability that the second card is greater than 7, without putting the first card back.

If the first card was 7, we have the options now: 8, 9.

Favorable outcome: 8, 9

Number of favorable outcomes: 2

Total possible outcomes: 8, 9

Number of total outcomes: 2

Then, the probability is of picking a number greater than 7:

$P(picking\text{ }a\text{ number greater than }7)=\frac{2}{2}=1$

Finally, let's calculate the probability of picking a 7 and then picking a number greater than 7​ (without putting the first card back).

$\begin{gathered} P=\frac{1}{3}*1 \\ P=\frac{1}{3} \end{gathered}$

Answer: The probability is 1/3.