if you draw one card from the deck then roll fair dice and finally flip one fair coin what is the probability that you get an even numbered card or heads on the coin or both?
There are 5 even numbered cards in a 52 card deck.
Either/Or Probability for Overlapping Events The probability that either of two events occurs is equal to the sum of the probabilities of the two events, minus the joint probability of the two events happening together. Also known as the "General Addition Rule".
To find the probability of getting an even numbered card or heads on the coin (or both), we need to analyze each event separately and then combine their probabilities.
1. Probability of getting an even numbered card:
A standard deck of cards contains 52 cards, with 26 of them being even numbered cards (2, 4, 6, 8, 10) and the other 26 being odd numbered cards. Since you draw one card from the deck, the probability of drawing an even numbered card would be 26/52, which simplifies to 1/2.
2. Probability of getting heads on the coin:
A fair coin has two equally likely outcomes - heads or tails. So, the probability of getting heads would be 1/2.
Now, to find the probability of both events occurring (getting an even numbered card and heads on the coin), we need to multiply their individual probabilities. Using the multiplication rule of probability, we multiply 1/2 (even numbered card) by 1/2 (heads on the coin):
(1/2) * (1/2) = 1/4
Therefore, the probability of getting an even numbered card or heads on the coin (or both) is 1/4 or 0.25, which can also be expressed as 25%.