The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
What is the probability that a card drawn at random from a deck of cards will be an ace? Since of the 52 cards in the deck, 4 are aces, the probability is 4/52 or 1/13.
The same principle can be applied to the problem of determining the probability of obtaining different totals from a pair of dice. As shown below, there are 36 possible outcomes when a pair of dice is thrown.
What is the probability of throwing a total greater than 8?
Calculate the probability of fewer than 5 sales.
Assume that there are n people in the room. Ignoring leap years, what is the probability that no one else in the room shares your birthday?
Assume that there are 253 people in the room. Ignoring leap years, what is the probability that no one else in the room shares your birthday? What is the probability that someone else in the room shares your birthday?
Assume that there are n people in the room. Ignoring leap years, what value of n (most closely) makes the probability that someone else shares your birthday (1/n)?
A women who is bright, single, 31 years old, outspoken and concerned with issues of social justice is most likely to be a.A bank teller b.A bank teller and a feminist
Over the course of a year, for which type of hospital would you expect there to be more days on which at least two thirds of the babies born were boys. a.a large hospital b.a small hospital c.it makes no difference
In a family of six children the sequence BGGBGB is__?___as BBBBGB a.more likely b.less likely c.the same as
The average score for all secondary students in a district is known to be 400. You pick a random sample of 10 students. The first student you pick had a score of 250. What would you expect the average to be for the other 9? a.more than 400 b.less than 400 c.400
The average score for all secondary students in a district is known to be 400. You pick a random sample of 10 students. The first student you pick had a score of 250. What would you expect the average to be for the entire sample of 10? a.more than 400 b.less than 400 c.400
Three girls have respective probabilities of 0.8, 0.6 and 0.7 of independently passing an examination. Find the probability that All pass None pass At least one passes Just one passes
Which is more likely? A man a.had a heart attack and is over 55, b. had a heart attack given that he is over 55.
Here's a puzzler for you all: You and two of your friends get into a dispute and decide to solve it with a "truel", a three way duel. Friend #1 is a crack shot, never missing his target. Friend #2 hits his target 2/3 of the time. You hit your target 1/3 of the time.
The truel It is decided that you will take the first shot, the 2/3 marksman will take the second shot (if still alive) and the 100% marksman will go last. This will continue until there is only one left alive.
The ‘truel’ On your turn you get to fire one bullet. You get to go first. In order to maximize your chances of living thru this, where should you take your opening shot? And what are your chances of winning the truel if you follow this strategy?
Duck Hunting! Ten duck hunters are all perfect shots 10 ducks fly over. All 10 hunters pick a duck at random to shoot at, all 10 hunters fire at the same time.
Duck Hunting! How many ducks could be expected to escape, on average, if this experiment were repeated a large number of times?
Definition A conditional probability is the probability of an event given that another event has occurred.
For example, what is the probability that the total of two dice will be greater than 8 given that the first die is a 6? There are 6 outcomes for which the first die is a 6, and of these, there are four that total more than 8
If A and B are two events then the conditional probability of A given B is
Definition In probability theory, two events are independent if the occurrence of one is unrelated to the probability of the occurrence of the other. Getting heads the second time a fair coin is tossed is independent of getting heads on the first toss. There is simply no valid way to predict the second outcome from knowledge of the first.
A and B are two events. If A and B are independent, then the probability that events A and B both occur is: p(A and B) = p(A) x p(B). In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B.
If A and B are Not Independent If A and B are not independent, then the probability of A and B is p(A and B) = p(A) x p(B|A) where p(B|A) is the conditional probability of B given A.
Consider the probability of rolling a die twice and getting a 6 on at least one of the rolls. The events are defined in the following way : Event A: 6 on the first roll: p(A) = 1/6 Event B: 6 on the second roll: p(B) = 1/6 p(A and B) = 1/6 x 1/6 p(A or B) = 1/6 + 1/6 - 1/6 x 1/6 = 11/36
Alternate approach The probability of getting a number from 1 to 5 on the first roll is 5/6. Likewise, the probability of getting a number from 1 to 5 on the second roll is 5/6. Therefore, the probability of getting a number from 1 to 5 on both rolls is: 5/6 x 5/6 = 25/36. This means that the probability of not getting a 1 to 5 on both rolls (getting a 6 on at least one roll) is: 1-25/36 = 11/36.
Despite the convoluted nature of this method, it has the advantage of being easy to generalize to three or more events. For example, the probability of rolling a die three times and getting a six on at least one of the three rolls is: 1 - 5/6 x 5/6 x 5/6 = 0.421