6 red pens & 4 blue pens are in a box. You draw one and keep it. Bob draws &keeps one. What is the probability of both pens being red.

Question

6 red pens & 4 blue pens are in a box. You draw one and keep it. Bob draws &keeps one. What is the probability of both pens being red.

Answer 1

Your draw: 6/10

Bob's draw: 5/9

 

(6/10)(5/9)

30 / 90

1 / 3

Answer 2

In addition to Mark M's answer, I think it helps to start with easy problems (small numbers) and to see all the outcomes.

Note:   Probability = (number of desired outcomes) / (number of total outcomes)

 

Number the pens R1-R6 and B1-B4 and represent (your draw)-(Bob's draw):

R1-R2  R1-R3  R1-R4  R1-R5  R1-R6  R1-B1  R1-B2  R1-B3  R1-B4
R2-R1  R2-R3  R2-R4  R2-R5  R2-R6  R2-B1  R2-B2  R2-B3  R2-B4
R3-R1  R3-R2  R3-R4  R3-R5  R3-R6  R3-B1  R3-B2  R3-B3  R3-B4
R4-R1  R4-R2  R4-R3  R4-R5  R4-R6  R4-B1  R4-B2  R4-B3  R4-B4
R5-R1  R5-R2  R5-R3  R5-R4  R5-R6  R5-B1  R5-B2  R5-B3  R5-B4
R6-R1  R6-R2  R6-R3  R6-R4  R6-R5  R6-B1  R6-B2  R6-B3  R6-B4
B1-R1   B1-R2   B1-R3   B1-R4   B1-R5   B1-R6  B1-B2  B1-B3  B1-B4
B2-R1   B2-R2   B2-R3   B2-R4   B2-R5   B2-R6  B2-B1  B2-B3  B2-B4
B3-R1   B3-R2   B3-R3   B3-R4   B3-R5   B3-R6  B3-B1  B3-B2  B3-B4
B4-R1   B4-R2   B4-R3   B4-R4   B4-R5   B4-R6  B4-B1  B4-B2  B4-B3

 

There are 90 possibilities and 30 have two reds.  Probability 30/90 = 1/3