Please help.
Find the probability of getting 2 hearts if the cards are drawn from a regular deck and the first card is not replaced.
A true/false quiz consists of twenty questions. If a student answers the twenty questions by making random guesses, what is the probability of getting at least one correct answer?
The first answer is (13/52) x (12/51). That is the probability of two successive draws of hearts.
For the second question, subtract from 1 the probablity of betting none right in 20 attempts. That will leave you with the probabilty of getting at least 1 right.
1 - (1/2)^20 = ?
1 - 1/2 ^20 = 0.999999046
and the first answer is 1/17
To find the probability of getting 2 hearts from a deck without replacement, you need to consider the number of heart cards and the total number of cards in the deck.
First, you find the probability of drawing a heart card on the first draw, which is 13 hearts out of 52 cards, so it is 13/52.
Then, for the second draw, since the first card was not replaced, there will be one less card in the deck. Now, you need to find the probability of drawing another heart card from the remaining 51 cards, which is 12/51.
To find the overall probability, you multiply the probabilities of the individual draws: (13/52) x (12/51) = 1/17.
Therefore, the probability of getting 2 hearts is 1/17.
For the second question about the true/false quiz, let's calculate the probability of getting at least one correct answer when making random guesses.
If the student randomly guesses the answers to the twenty questions, there are two possible outcomes for each question: correct or incorrect. So, the probability of getting a correct answer for each question is 1/2.
To find the probability of getting at least one correct answer, we need to subtract from 1 the probability of getting none right in 20 attempts.
The probability of getting none right in one attempt is 1/2, and since the student has to answer 20 questions independently, the probability of getting none right in 20 attempts is (1/2)^20.
Therefore, the probability of getting at least one correct answer is:
1 - (1/2)^20 = 1 - 0.00000095367 = 0.999999046.
So, the probability of getting at least one correct answer in the quiz is approximately 0.999999046, or very close to 1.