There is 10 a stack of cards, each given a different number 1 from 10 to . Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is less than 4?
there are 5 odd numbers, and 3 cards less than 4, so since the events are independent, the probability of both is
5/10 * 3/10 = 3/20
To find the probability that the first card is an odd number and the second card is less than 4, we need to determine the probability of each event and then multiply them together.
Event 1: Probability of selecting an odd number as the first card
Out of the cards numbered 1 to 10, there are 5 odd numbers (1, 3, 5, 7, 9) and 10 total cards. Therefore, the probability of selecting an odd number as the first card is 5/10 or 1/2.
Event 2: Probability of selecting a number less than 4 as the second card
There are 3 cards (1, 2, 3) that are less than 4 out of the remaining 10 cards. Since we are replacing the first card, the total number of cards remains the same. Therefore, the probability of selecting a number less than 4 as the second card is 3/10.
To find the overall probability, we multiply the probabilities of each event together:
Probability = (Probability of Event 1) × (Probability of Event 2)
= (1/2) × (3/10)
= 3/20
Therefore, the probability that the first card is an odd number and the second card is less than 4 is 3/20.
To determine the probability, we need to first calculate the total number of possible outcomes and then determine the number of favorable outcomes.
Total number of possible outcomes:
Since there are 10 cards in the stack, we have 10 possible choices for the first card. After replacing the card, we still have 10 possible choices for the second card. Therefore, the total number of possible outcomes is 10 * 10 = 100.
Number of favorable outcomes:
We want the first card to be an odd number and the second card to be less than 4.
For the first card, there are 5 odd numbers in the stack (1, 3, 5, 7, 9), so we have 5 possible choices.
For the second card, there are 3 numbers less than 4 in the stack (1, 2, 3), so we have 3 possible choices.
Therefore, the number of favorable outcomes is 5 * 3 = 15.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 15 / 100
= 0.15
So, the probability that the first card is an odd number and the second card is less than 4 is 0.15 or 15%.