3 years ago

What is the likelihood that the children in square 2 will have earlobes that are not attached?

Mathematics

1 answer:

notka56 [123]3 years ago

4 0

Answer : 2/4 children will have earlobes that are not attached

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The number of customers waiting for gift-wrap service at a department store is an rv X with possible values 0, 1, 2, 3, 4 and co

FrozenT [24]

Let $Y_i$ denote the number of packages brought by customer $i$ . If, for instance, $X=2$ customers are in line, then the total number of packages is $Y=Y_1+Y_2$ , and

$P(Y=y)=P(Y_1=y_1,Y_2=y_2)=P(Y_1=y_1)P(Y_2=y_2)$

since the number of packages brought by any customer is independent from the number of packages brought by any other.

a. $P(X=3,Y=3)$ is the probability that a total of 3 packages are waiting to get wrapped from among a total of 3 customers. This means each customer must have exactly one package. So

$P(X=3,Y=3)=P(X=3)P(Y=3)^3\approx0.0416$

b. $P(X=4,Y=11)$ is the probability that a total of 11 packages are brought by 4 customers. The only way for there to be 11 packages is if 3 customers bring 3 packages and the last 1 brings 2. There are $\dbinom43=4$ ways this can happen, so