Can Someone Please Help and Teach me How to Solve This Problem? Please!
A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4, and 5. The cards are well shuffled and you randomly draw one card.
R=card drawn is red
E=card drawn is even-numbered
a. How many elements are there in the sample space?
b. P(E)=
Of course, I'd be happy to help you solve this problem!
To find the answer, we need to break it down into smaller steps.
a. To determine the number of elements in the sample space, we have to consider all possible outcomes. In this case, our outcomes are the cards that can be drawn from the deck.
There are 6 red cards and 5 black cards, so the total number of cards in the deck is 6 + 5 = 11. Therefore, there are 11 possible outcomes in the sample space.
b. To calculate the probability P(E) (the probability of drawing an even-numbered card), we need to find the number of favorable outcomes (even-numbered cards) and divide it by the total number of outcomes.
There are three even-numbered red cards (2, 4, and 6) and two even-numbered black cards (2 and 4). So the total number of even-numbered cards is 3 + 2 = 5.
From part a, we know that there are 11 possible outcomes in the sample space.
Therefore, P(E) = number of favorable outcomes / total number of outcomes = 5/11.
So the probability of drawing an even-numbered card is 5/11.
I hope this explanation helps you understand how to solve the problem!