7.06 Applications of probability

Find the probability of picking the ten of diamonds from a standard deck of cards.

A local raffle prize will be given to the person who has the winning number from one of the 200 tickets sold. Find the probability of winning the raffle if you purchase 30 tickets.

In a card game, Aaron is dealt a hand of two cards from a standard deck of 52 cards.

In Monopoly, each player rolls two dice on their turn. The sum of the two dice tells them how many squares they move. It is Beth's turn and she is 5 squares away from “Free Parking”, where she wants to land. What is the probability that she will land on “Free Parking” on this turn?

Christa enters a competition in which she guesses the 3-digit code (from 000 to 999) which cracks open a vault containing one million dollars. If the 3-digit number to open the vault is randomly generated by a computer, find the probability that it is:

In a game of Blackjack, a player is dealt a hand of two cards from the same standard deck. Find the probability that the hand dealt:

In a game of Draw Poker, a player is dealt a hand of 5 cards from the same deck.

In a game of Monopoly, rolling a double means rolling the same number on both dice. When you roll a double this allows you to have another turn. Find the probability that Sarah rolls:

In a game of Yahtzee, each player rolls 5 dice. A player rolls two of the dice and gets 2 sixes. The player still needs to roll the other 3 dice. Find the probability that they will get:

In a game of Draw Poker, a player is dealt a hand of 5 cards where each card is dealt from a brand new deck. Find the probability of being dealt a:

One of the better hands in poker is a "two pair", where a pair is two cards that have the same number or value. For example, two threes will form a pair. I draw four cards from a standard deck, and they consist of one pair and two other cards that don't match with any card in my hand.

If I draw another card, what is the probability that this card will give me a second pair?

One of the better hands in poker is a "three of a kind", where cards are the same number or value. For example, three fours makes three of a kind. I am dealt four cards from a standard deck consisting of one pair and two other cards that do not match any of my other cards.

If I draw another card from the remaining deck, what is the probability that this card will give me three of a kind?

One of the better hands in poker is a flush, where all five cards are of the same suit. If I have three spades already and am about to draw two cards, what is the probability that I will get a flush?

A jar contains 7 blue M&M’s and 5 red M&M’s. Bob takes one from the jar and does not replace it. Luke then takes an M&M from the jar. If it is the same colour as Bob’s, Luke wins the jar of M&M's.

Find the probability that Luke wins the jar.

A traffic light pole with green, red and yellow lights is set up on a race track. A race car approaching the pole is equally likely to see a green, red or yellow light.

Select the best reason for this:

A set of traffic lights is red for half the time, orange for \dfrac{1}{5} of the time and green for the rest of the time. Find the probablity that the traffic light is green.

A traffic light is green for 35 seconds, yellow for 5 seconds and then red for 50 seconds. Find the probability that the next person at the traffic lights gets a:

At a particular traffic light, it was found that the light in a particular direction stays green for 119 seconds, yellow for 5 seconds and red for 76 seconds.

If a car approaches the traffic light, find the probability, as a percentage, that the light will be:

At a railway crossing, there is only a red and green light, and they stay on for the same amount of time.

On the island of Timbuktoo, the probability that a set of traffic lights shows red, yellow or green is equally likely. Christa is travelling down a road where there are two sets of traffic lights.

Consider the tree diagram that indicates the possible pairs of traffic light signals:

A traffic light at a railway crossing has a chance of 0.3 of being yellow. Three cars approach the light separately at different times throughout the day.

Find the probability that all three cars approach a yellow light.

At an intersection, the traffic lights for different directions each have a probability of 0.35 of being green. Two cars travelling in different directions arrive at the traffic lights at the same time.

Find the probability that:

Every 60 seconds, a traffic light remains green for 34 seconds, yellow for 3 seconds and red for 23 seconds.

Tina is at point A driving in the direction of point B. There are traffic lights at points B, C, D and E, and the probability of a green light at any one of these is 0.4.

If Tina arrives at a traffic light when it is green, she will go straight. If it is not green, she will turn right. She does not turn left or drive back in the direction of A at any time.

The data below shows the time spent waiting for a green light at a set of traffic lights, in seconds: