GOODMAN Group Title Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that both cards are greater than 2 and less than 9? 2 years ago 2 years ago

1. ParthKohli Group Title

2. GOODMAN Group Title

Thanks little bro, lol. I am studying and forgot this all.

3. ParthKohli Group Title

What would be the probability of getting a card between 2 and 9 in the first pick?

4. GOODMAN Group Title

2/52 and 9/52

5. ParthKohli Group Title

No...it's saying that it's greater than 2 and less than 9. 3,4,5,6,7,8 are the numbers that qualify for me :)

6. GOODMAN Group Title

So we have to get the ones in between?

7. ParthKohli Group Title

Yes.. exactly

8. ParthKohli Group Title

Since there are 3,4,5,6,7,8 in four suits, the probability would be: $$\color{Black}{\Rightarrow \Large {4 \times 6 \over 52} }$$ For the first pick.

9. ParthKohli Group Title

Simplifying further: $$\color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }$$

10. ParthKohli Group Title

Now we've picked the first. We have 1 card LESS in the deck because we haven't replaced the cards.

11. ParthKohli Group Title

So this time the denominator of the probability would become 51. The numerator will also get one less because we have assumed that we have picked one card which is 3,4,5,6,7 or 8.

12. ParthKohli Group Title

There are 23 cards left that we want. 51 total cards left. $$\color{Black}{\Rightarrow \Large {23 \over 51} }$$

13. GOODMAN Group Title

Okay...so since we had not replaced, we have to subtract 1?

14. ParthKohli Group Title

Now if we want two things to happen at the same time, we shall multiply the probabilities. $$\color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}$$

15. ParthKohli Group Title

We have to subtract 1 from both numerator and denominator.

16. GOODMAN Group Title

Thats it?

17. ParthKohli Group Title

Nope

18. GOODMAN Group Title

Wait. so after we multiply, we have to simplify further too?

19. ParthKohli Group Title

Oops.. I meant this: $$\color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}$$

20. ParthKohli Group Title

Multiply the fractions. The fractions are in their simplest forms so when we'll multiply it'd be in the simplest form.

21. GOODMAN Group Title

Yes, i did that. Okay, so 46/221 is final answer?

22. ParthKohli Group Title

How did you get that?

23. ParthKohli Group Title

Oh yes

24. ParthKohli Group Title

$$\color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }$$

25. ParthKohli Group Title

Correct! :D

26. GOODMAN Group Title

Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/

27. ParthKohli Group Title

Haha probability is easy...getting the hang of what it involves is important

28. GOODMAN Group Title

Yea, see, im reviewing this since last semester, lol.

29. ParthKohli Group Title

And I've helped someone on this site after a long time. we usually just answer questions ://

30. GOODMAN Group Title

Thanks, I actually learned :D