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

Answer:  $\dfrac{3}{25}$

Step-by-step explanation:

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

Then, probability that he first draw a black sock : P(black)$=\dfrac{1}{5}$

Since we replaced first sock , then the total number of socks in bag remains the same i.e. 5.

Probability that he draw a red sock : P(red)$\dfrac{3}{5}$

Since both the events are independent , thus

P(black then red)=P(Black) P(red)

$=\dfrac{1}{5}\cdot\dfrac{3}{5}=\dfrac{3}{25}$

Hence, the probability that he will draw a black sock and then a red sock=$\dfrac{3}{25}$