Question

Directions: Calculate each conditional probability. Show all work and write the answer as a reduced fraction, unless otherwise specified.1. What is the formula for finding the conditional probability of event  occurring, given that event  has already occurred?2. If the first card selected is a red card, what is the probability of selecting a black card on the second draw from a standard deck of cards? Write the probability as a percentage.3. There are 6 red, 5 white, 3 blue, and 4 green marbles in a bag. What is the probability of selecting a white marble, if a white marble has already been selected?4. There are 6 red, 5 white, 3 blue, and 4 green marbles in a bag. What is the probability of selecting a red marble, given that a blue marble was already selected?5. While playing Blackjack, an Ace is dealt. To get Blackjack, or 21, a card worth 10 is needed. This could be a 10, Jack, Queen, or King. What is the probability of not getting Blackjack?

Answer 1

Conditional probability is the probability of an event occurring given that another event has already occurred, and its given by the formula:

`\begin{gathered} P(A|B)=(P(A\cap B))/(P(B)) \\ P(A|B)=\text{ the conditional probability} \\ P(A\cap B)=\text{ joint probability of events A and B} \\ P(B)=\text{ the probability of event B} \end{gathered}`

If the first card is red and the second card is black:

P(1st red and 2nd black)= P(1st red) x P(2nd black)

`(26)/(52)*(26)/(51)=(13)/(51)*100=25.5\text{ percent}`

So, there are 18 marbles in the bag:

Probability of selecting a white marble=

`(4)/(17)*100=23.5\text{ percent}`