given a deck of ten cards numbreed one through ten ,whats the probability of selecting an even card, not replacing it in the deck , and then selecting a five
given a deck of ten cards numbered one through ten, whats the probability of selecting an even card, not replacing it in the deck ,and then selecting a five
To determine the probability of selecting an even card from a deck of ten cards, not replacing it, and then selecting a five, we need to break it down step by step:
Step 1: Calculate the probability of selecting an even card.
Out of the ten cards, half of them are even numbers (2, 4, 6, 8, and 10), and the other half are odd numbers (1, 3, 5, 7, and 9). So the probability of selecting an even card on the first draw is 5/10 or 1/2.
Step 2: Calculate the conditional probability of selecting a five, given that an even card was already selected.
Once an even card is selected and not replaced, we are left with four even cards (2, 4, 6, and 8) and one odd card (5). So the probability of selecting a five from the remaining cards is 1/5.
Step 3: Calculate the overall probability by multiplying the individual probabilities.
To find the probability of both events happening, we multiply the probabilities from step 1 and step 2.
P(Even card and then a five) = P(Even card) * P(Five|Even card)
= (1/2) * (1/5)
= 1/10
Therefore, the probability of selecting an even card, not replacing it, and then selecting a five is 1/10 or 0.1.