Question

In: Statistics and Probability

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters....

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of randomly selecting one of the highlighters and recording its color. Find the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected.

Expert Solution

The probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected.

Given that Yellow highlight is selected, Therefore probability that that a blue or yellow highlighter = 1 because given that selected highlighter is Yellow , then the event of selecting a blue or yellow highlighter is certain.

The probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected = 1

Formula for a conditional probability :

$P(A|B) = \frac{P(A \; and\; B) }{P(B)}$

Y : Event of selecting a Yellow highlighter

P(Y) = Probability of selecting a Yellow highlighter

B : Event of selecting a Blue highlighter

P(B) = Probability of selecting a blue highlighter

The probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected = P((Y or B)|Y)

Applying the above formula

$P((Y or B)|Y)= \frac{P((Y\; or\; B)\; and\; Y)}{P(Y)}$

(Y or B) and Y = Y

P((Y or B) and Y) = P(Y)

$P((Y or B)|Y)= \frac{P((Y\; or\; B)\; and\; Y)}{P(Y)}=\frac{P(Y)}{P(Y)}=1$

The probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected = 1

orchestra answered 2 years ago

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