Answer: P = 0.125 = 1/8
Step-by-step explanation:
We know that he has a blue coat and a black coat.
If he dresses at random, then the probability of getting the blue coat is equal to the quotient between the number of blue coats (1) and the total number of coats (2).
Then the probability is:
p = 1/2
We also know that he has blue pants and brown pants, the probability of getting at random the blue pants is calculated in the same way than above, then:
q = 1/2
And for the shirt he has a blue shirt and a red one, the probability of randomly selecting the blue one is calculated in the same way than above, then:
k = 1/2
Now, the joint probability (he selects all blue clothes) is equal to the product of the individual probabilities:
P = p*q*k = (1/2)*(1/2)*(1/2) = 1/8 = 0.125
