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?

The fraction is 19/40

Step-by-step 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:

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:

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:

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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