In your sock drawer you have 6 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them on.
1. Find the probability you end up wearing the following socks. (Round your answers to four decimal places.)
a) 2 blue socks.
b) no gray socks.
c) at least 1 black sock.
d) matching socks.

a) 0.1429

b) 0.2667

c) 0.3067

d) 0.3524

Step-by-step explanation:

Blue = 6

Gray = 7

Black = 2

Number of socks = 15

a) 2 blue socks.

The probability of getting two consecutive blue socks is:

b) no gray socks.

The probability of getting no grey socks with two picks is:

c) at least 1 black sock.

The probability of getting at least one black sock is:

d) matching socks.

The probability of getting matching socks is the sum of the probabilities of getting 2 black, 2 blue or 2 gray socks:

blue marble is 15 times out of 50 = 15/50 reduces to 3/10

landing on tails is 24 out of 50 = 24/50 reduces to 12/25

to find the probability of both multiply together:

3/10 x 12/25 = 3 x 12 / 10 x 25 = 36/250

if you multiplied the numerator and denominator by 10 you get 360/2500.

the answer is 360/2500

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2