Question

the numbers 2-12 are written on cards and placed in the bag.what is the probability of picking an even number then replacing it and then picking a 7?

Answer 1

We have the cards numbered as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Sample number is, n(S)=11.

We pick a card and want to get even number like 2, 4, 6, 8, 10, and 12.

Probability of picking an even number would be :-

P(even numbers) = $\frac{6}{11}$

Now we replace the card and want to get a 7 in second attempt.

Probability of picking a 7 would be :-

P(number 7) = $\frac{1}{11}$

Now Probability of this event = P(even numbers) × P(number 7)

Probability = $(\frac{6}{11} )(\frac{1}{11} ) = \frac{6}{121}$

So final answer is $\frac{6}{121}$.