Question

Liam has 4 black shirts and 6 white shirts in his closet. He also has 5 black ties and 3 white ties in his drawer. If Liam reaches into the closet and takes out a shirt at random, then reaches into the drawer and takes out a tie at random, then the probability that the shirt and the tie are the same color can be written as a fraction a/b. What is such fraction?

Answer 1

The fraction is 19/40

Explanation:

The probability that the shirt and the tie are the same color is the sum of probability that Liam choose a white shirt and a white tie with the probability that Liam choose a Black shirt and a Black tie.

So, The probability that Liam choose a white shirt and a white tie is:

`(6)/(10) *(3)/(8) =(9)/(40)`

Because Liam has 10 shirts and 6 of them are white and Liam has 8 ties and 3 of them are white.

At the same way, the probability that Liam choose a Black shirt and a Black tie is:

`(4)/(10) *(5)/(8) =(1)/(4)`

Because Liam has 10 shirts and 4 of them are black and Liam has 8 ties and 5 of them are black.

Finally, The probability that the shirt and the tie are the same color is:

`(9)/(40) +(1)/(4)=(19)/(40)`