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How to calculate the probability of winning the second prize?
So the probability of winning the second prize is (6C5)(42C1) 48C6 = 252 12271512 ≈0.0000205 ( 6 C 5) ( 42 C 1) 48 C 6 = 252 12271512 ≈ 0.0000205 A multiple-choice question on an economics quiz contains 10 questions with five possible answers each. Compute the probability of randomly guessing the answers and getting exactly 9 questions correct.
What is the number of ordered arrangements in a permutation?
A permutation is an ordered arrangement. The number of ordered arrangements of r objects taken from n unlike objects is: n P r = n! . (n – r)! In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10.
What is the probability that someone will not share your birthday?
There are 365 days in the year (let’s ignore leap years) and removing your birthday from contention, there are 364 choices that will guarantee that you do not share a birthday with this person, so the probability that the second person does not share your birthday is 364/365. Now we move to the third person.
How to calculate the probability of drawing five cards?
Compute the probability of randomly drawing five cards from a deck and getting exactly two Aces. The solution is similar to the previous example, except now we are choosing 2 Aces out of 4 and 3 non-Aces out of 48; the denominator remains the same:
Where does the numerator go in a probability formula?
This number will go in the denominator of our probability formula, since it is the number of possible outcomes. For the numerator, we need the number of ways to draw one Ace and four other cards (none of them Aces) from the deck. Since there are four Aces and we want exactly one of them, there will be
What is the probability of an intersection of two events?
The intersection of events A and B, written as P(A ∩ B) or P(A AND B) is the joint probability of at least two events, shown below in a Venn diagram. In the case where A and B are mutually exclusive events, P(A ∩ B) = 0.
What is the probability of A and B being mutually exclusive?
In the case where A and B are mutually exclusive events, P (A ∩ B) = 0. Consider the probability of rolling a 4 and 6 on a single roll of a die; it is not possible. These events would therefore be considered mutually exclusive.