0

How do you do this? So, I was doing a mini maths test and the question popped up. Because there were 4 kings, so I did 4/52(there were 52 cards) and then simplified it. I got it wrong. So confused! (No replacement, but it will be great if you guys show me with replacement as well).

TempzApex
  • 111

2 Answers2

1

Hint: this can be solved using a “probability tree”

  • start by drawing the first card. What are the odds of it being a king? Simply $4/52$.
  • Now that you were lucky enough to draw the first king there are only ... kings left in the deck of only ... cards.
  • Conclude.
b00n heT
  • 16,360
  • 1
  • 36
  • 46
1

I will give another way to think about this problem, which might help the OP.

The sample space in this problem is ${52}\choose{2}$ since there are ${52}\choose{2}$ ways to pick a pair of cards. There are 4 kings, therefore there are ${4}\choose{2}$ ways of picking a pair of kings. From here we see that the probability of getting 2 kings is

$$P(\textrm{getting 2 kings }) = \frac{\textrm{number of ways the desired event can occur}}{\textrm{number of possible outcomes}}=\frac{{4}\choose{2}}{{52}\choose{2}}$$

  • Why is it (4/2) and (52/2) instead of (2/4) and (2/52)? – TempzApex Dec 02 '20 at 07:54
  • it is not a division, it is "4 choose 2" which is the amount of way you can pick 2 thing from a group of 4. If you are not familiar with this concept you can read this: https://en.wikipedia.org/wiki/Combination#:~:text=Combinations%20refer%20to%20the%20combination,with%20repetition%20are%20often%20used. – Samael Manasseh Dec 02 '20 at 14:26