Identify whether the following events are independent or dependent:
A person runs a marathon, and then falls ill from exhaustion.
A card is randomly selected from a normal deck of cards, and then returned to the deck. The deck is shuffled and another card is selected.
Each student is allowed to randomly pick an item from the teacher's prize bag.
The probability of two independent events, A and B are, P \left( A \right) = 0.5 and P \left( B \right) = 0.8. Determine the probability of:
Both A and B occurring.
Neither A nor B.
A or B or both.
B but not A.
A given that B occurs.
A standard six-sided die is rolled 691 times.
If it lands on a six 100 times, find the probability that the next roll will land on a six.
State whether the outcome of the next roll is independent of or dependent on the outcomes of previous rolls.
Ursula takes a bus to the station and then immediately gets on a train to work. Is the probability of her missing the train independent or dependent on her missing her bus?
On a roulette table, a ball can land on one of 18 red or 18 black numbers.
If it lands on a red number on the first go, find the probability that it will land on a red number on the second go.
Are the successive events of twice landing on a red number dependent or independent?
From a standard pack of cards, 1 card is randomly drawn and then put back into the pack. A second card is then drawn.
Find the probability that neither of the cards are spades.
Find the probability that at least 1 of the cards is a spade.
Mae deals two cards from a normal deck of cards. Calculate the probability that she deals:
Two 10s.
Two red cards.
Two diamonds.
A 10 of spades and an Ace of diamonds, in that order.
A 10 of clubs and an Ace of spades, in any order.
Two standard die are rolled. One is red and one is white. Calculate the probability that:
The same number is rolled.
The sum of the two outcomes exceeds 9.
The red die is 4 and the white die 6.
The red die is even and the white die is odd.
The sum of the two outcomes is less than 2.
Two events A and B are such that P \left( A \cap B \right) = 0.3 and P \left( A \right) = 0.5.
Calculate P \left( B \right) if events A and B are independent.
For the following Venn diagrams:
Calculate the value of x.
State whether the events A and B are mutually exclusive.
Suppose P \left( A \right) = 0.2 and P \left( B \right) = 0.3.
Find the maximum possible value of P \left( A \cup B \right).
Identify events A and B as mutually exclusive or independent.
Find the minimum possible value of P \left( A \cup B \right).
Two events A and B are such that: P \left( A \cap B \right) = 0.04 and P \left( A \right) = 0.4.
If P \left( B \right) = 0.1, state whether the events A and B independent.
State whether the events A and B mutually exclusive.
Suppose P \left( A \cup B \right) = 0.4, P \left( A' \right) = 0.7 and P \left( B' \right) = 0.8.
Find P \left( A \cap B' \right).
Find P \left( B \cap A' \right).
Determine P \left( A \cap B \right).
State whether events A and B are mutually exclusive.
Find the probability of drawing a green counter from a bag of 9 green counters and 6 black counters, replacing it and drawing another green counter.
A number game uses a basket with 8 balls, all labelled with numbers from 1 to 8. Three balls are drawn at random, with replacement.
Find the probability that the ball labelled 4 is picked:
Exactly once
Exactly twice
Exactly three times.
Eileen randomly selects two cards, with replacement, from a normal deck of cards. Calculate the probability that both cards are:
Red
The same colour.
Different colours.
Christa randomly selects two cards, with replacement, from a normal deck of cards.
Calculate the probability that:
The first card is a Queen of Diamonds and the second card is a 10 of Spades.
The first card is Diamonds and the second card is a 10.
The first card is a Queen and the second card is black.
The first card is not a 7 and the second card is not Spades.
Valentina randomly selects three cards, with replacement, from a normal deck of cards. Find the probability that:
The cards are five of clubs, King of clubs, and Jack of spades, in that order.
The cards are all red.
The first card is a 2, the second card is a spade and the third card is red.
The cards are all spade.
None of the cards is a 8.
In a lottery there are 37 balls.
Find the probability of a particular ball being drawn first.
A ball is discarded after it has been drawn. If ball number 22 is drawn on the first go, find the probability of ball number 15 being drawn next.
Is the probability of each successive ball drawn the same as the probability of the first ball drawn?
Determine whether the draws are dependent or independent events.
Two cards are to be chosen from a pack of cards numbered 1 to 11. Find the probability of drawing a 1, 2 or 3 first, and after replacing the card, drawing a 9, 10 or 11.
Three marbles are randomly drawn with replacement from a bag containing 6 red, 5 yellow, 6 white, 1 black and 3 green marbles. Find the probability of drawing:
Three white marbles.
No green marbles.
At least 1 red marble.
At least 1 white marble.
There are 4 blue counters and 6 brown counters in a bag. Find the probability of choosing a blue counter, not replacing it, then choosing a brown counter.
A number game uses a basket with 10 balls, all labelled with numbers from 1 to 10. Two balls are drawn at random.
Find the probability that the ball labelled 2 is picked once if the balls are drawn:
With replacement.
Without replacement.
A standard deck of cards is used and 3 cards are drawn out.
Find the probability that all 3 cards are clubs if the cards are drawn:
With replacement.
Without replacement.
A hand contains a 10, a jack, a queen, a king and an ace. Two cards are drawn from the hand at random, in succession and without replacement. Find the probability that:
The ace is drawn.
The king is not drawn.
The queen is the second card drawn.
A number game uses a basket with 5 balls, all labelled with numbers from 1 to 5. Three balls are drawn at random, without replacement.
Find the probability that the ball labelled 4 is picked.
Find the probability that the ball labelled 4 is picked and the ball labelled 1 is also picked.
From a set of 10 cards numbered 1 to 10, two cards are drawn at random without replacement. Find the probability that:
Both numbers are even.
One is even and the other is odd.
The sum of the numbers is 12.
Consider the word WOLLONGONG. If three letters are randomly selected from it without replacement, find the probability that:
The letters are W, O, L, in that order.
The letters are O, N, G, in that order.
All three letters are O.
None of the three letters is an O.
Three marbles are randomly drawn without replacement from a bag containing 6 red, 6 yellow, 6 white, 6 black and 4 green marbles. Find the probability of drawing:
Three white marbles.
Three black marbles.
Zero green marbles.
Zero yellow marbles.
At least one red marble.
Eileen randomly selects two cards, with replacement, from a normal deck of cards. Find the probability that:
The first card is a queen of spades and the second card is a 4 of clubs.
The first card is spades and the second card is a 4.
The first card is a Queen and the second card is black.
The first card is not a 7 and the second card is not Clubs.
Sarah has a box of Favourites chocolates. In this box there are 30 chocolates, 5 of which are Turkish Delights. Sarah takes and eats a chocolate without looking until she gets a Turkish Delight.
Find the probability she only eats one chocolate.
Find the probability she eats only two chocolates to the nearest percent.
Find the probability she eats five chocolates to the nearest percent.
As she eats more and more chocolates, state whether the probability of the next chocolate being a Turkish Delight is getting higher or lower.
How many chocolates must Sarah have eaten to be certain that the next chocolate will be a Turkish Delight?
Tom has shuffled a standard pack of 52 playing cards. He draws one card from the pack at a time, and then puts it aside. He will stop when he draws the 9 of Diamonds.
Find the probability he only has to draw exactly 1 card.
Find the probability he has to draw exactly 2 cards.
Find the probability he has to draw exactly 3 cards.
Find the probability Tom will stop after the 44th card.
As more cards are drawn that aren't the desired card, does the probability that the next card selected is the 9 of Diamonds increase or decrease?