Question

A person draws a card from a hat. Each card is one color with the following probabilities of being drawn: 1/10 for red, 1/5 for blue, 1/20 for black, and 1/5 for pink. What is the probability of pulling a blue or black card, written as a reduced fraction?

Answer 1

`(1)/(4)`

Explanation:

We are given that a card is drawn from a hat.

Probability that a red card is drawn, P(red) =
`(1)/(10)`

Probability that a blue card is drawn, P(blue) =
`(1)/(5)`

Probability that a black card is drawn, P(black) =
`(1)/(20)`

Probability that a pink card is drawn, P(pink) =
`(1)/(5)`

All these events are mutually exclusive i.e. they do not have anything in common.

For any two events A and B which are mutually exclusive, with probability P(A) and P(B), the probability that any one of the two events occur:

`P(A\cup B) = P(A) + P(B)`

Here event A can be thought of as drawing a blue card and

event B can be thought of as drawing a black card

So, P(blue or black) = P(blue) + P(black)

`\Rightarrow (1)/(5)+(1)/(20)\\\Rightarrow (4+1)/(20)\\\Rightarrow (5)/(20)\\\Rightarrow (1)/(4)`

So, the probability that a blue or black card is drawn from the hat:

`(1)/(4)`