Question

1. A particular slot machine in a casino has payouts set so that the probability of winning money in one play of the slot machine is 29%. Each game on the slot machine is independent of all other games played on that machine. If a player chooses to play three games in a row on this machine, what is the probability that he or she will win money in every one of those three games?

2. In a short string of holiday lights, when at least one bulb in the string stops working then all of the lights go out. Assume that each bulb works or fails independently of the other bulbs, and suppose that each bulb has a 98% chance of working throughout the holiday season. On a string of twelve bulbs, what is the probability that at least one bulb will stop working during the holiday season, making all of the lights go out on the string?

3. In a standard deck of 52 playing cards, the cards are broken down into 4 suits of 13 cards each. The 13 hearts and 13 diamonds are all red cards, while the 13 clubs and 13 spades are all black cards. If you shuffle the deck thoroughly and select one card at random, then what is P("your card is a red card" | "your card is a heart")?

4. A bag contains a total of 15 marbles -- eight orange, and seven blue. After mixing the marbles in the bag, you reach in and take one, then, without replacing that first marble, you reach in and take a second marble. What is the probability that both marbles you took are blue? Please give your answer as a decimal, rounded to two places after the decimal point.

Answer 1

1)

p = 0.29, n = 3

The required probability that he or she will win money in every one of those three games = = 0.0244

2)

The required probability = 1 - None of the bulb stops working

= = 0.2153

3)

The required probability = P(card is red card and card is heart)/P(card is a heart)

= (13/52)/(13/52) = 1

I.e A heart is always a red card

4)

The required probability = 7/15 * 6/14 = 0.2