Two cards are drawn at the same time from a 52-card deck. Dind the probability of each event.

a) both cards are jacks
b) both cards are sixes
c) eith both cards are jacks or both cards are sixes

PLEASE SHOW ALL WORK!

a)4/52 x 3/51 = 1/13 x 1/17 = 1/221

b) same

c) 2/221 (add the previous 2)

To find the probability of each event, we need to determine the number of favorable outcomes (cards that match the event) and divide it by the total number of possible outcomes (all the cards in the deck).

a) Both cards are jacks:
There are 4 jacks in a standard deck (one for each suit), and we are drawing 2 cards simultaneously. The number of favorable outcomes is the number of ways to choose 2 jacks from 4, which is calculated using the combination formula: C(4, 2) = 4! / (2! * (4 - 2)!) = 6.
The total number of possible outcomes is the number of ways to choose any 2 cards from a deck of 52, which is given by C(52, 2) = 52! / (2! * (52 - 2)!) = 1326.

Therefore, the probability of drawing two jacks is: P(a) = favorable outcomes / total outcomes = 6 / 1326 ≈ 0.0045.

b) Both cards are sixes:
There are 4 sixes in a standard deck (one for each suit), and again, we are drawing 2 cards simultaneously.
The number of favorable outcomes is the number of ways to choose 2 sixes from 4, which is calculated using the combination formula: C(4, 2) = 4! / (2! * (4 - 2)!) = 6.

Therefore, the probability of drawing two sixes is: P(b) = favorable outcomes / total outcomes = 6 / 1326 ≈ 0.0045.

c) Both cards are jacks or both cards are sixes:
In this case, we need to find the number of ways to choose 2 jacks and the number of ways to choose 2 sixes, and then add them together.
The number of ways to choose 2 jacks from 4 is 6, as we calculated before. Similarly, the number of ways to choose 2 sixes from 4 is also 6.

Therefore, the total number of favorable outcomes is 6 + 6 = 12.

Finally, the probability of drawing either 2 jacks or 2 sixes is: P(c) = favorable outcomes / total outcomes = 12 / 1326 ≈ 0.0090.

So, the probabilities are:
a) P(a) ≈ 0.0045
b) P(b) ≈ 0.0045
c) P(c) ≈ 0.0090.