Question

Luka has a bag containing 5 socks: 3 red, 1 white, and 1 black. He draws 1 sock out of the bag, replaces it, and then draws another sock.What is the probability that he will draw a black sock and then a red sock, P(black, then red)?

Answer 1

Prob( drawing a black sock) = 1/5

Prob ( drawing a red sock) = 3/5

These 2 events are independent so they are multiplied:-

P(black then red sock) = 1/5 * 3/5 = 3/25 Answer

Answer 2

the probability that he will draw a black sock and then a red sock, P(black, then red) is:

3/25=0.12

Explanation:

Luka has a bag containing 5 socks: 3 red, 1 white, and 1 black.

Let A denote the event of drawing a first black sock.

and B denote the event of drawing a second red sock.

Hence, A∩B denote the event of drawing a black and then a red sock.

As the drawing of a second sock is done by replacement.

Hence, the probability of two events is independent.

i.e. P(A∩B)=P(A)×P(B)

Now,

P(A)=1/5

(Since there are 1 black sock out of total 5 sock)

and P(B)=3/5

(Since there are a total of 3 red socks out of total 5 sock)

Hence,

P(A∩B)=(1/5)×(3/5)=3/25

Hence, the probability is:

3/25=0.12