You have the numbers 1- 10 in a bag.You draw a slip at random and draw another without replacing the first. Find the probability that both numbers are odd.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
5/10 * (5-1)/(10-1) = ?
To find the probability of drawing two odd numbers without replacement, we need to determine the total number of outcomes and the number of favorable outcomes.
First, let's calculate the total number of outcomes when drawing two numbers from a bag containing numbers 1-10. When drawing the first number, there are 10 possible outcomes (as there are 10 numbers in the bag). When drawing the second number, there are 9 remaining numbers in the bag, so there are 9 possible outcomes.
To determine the number of favorable outcomes, we consider that there are 5 odd numbers (1, 3, 5, 7, and 9) in the bag. When drawing the first number, we have 5 favorable outcomes. For the second number, since we didn't replace the first number, there are 4 favorable outcomes remaining.
Therefore, the number of favorable outcomes is 5 * 4 = 20.
The probability of drawing two odd numbers is given by the number of favorable outcomes divided by the total number of outcomes:
P(Both numbers are odd) = favorable outcomes / total outcomes
= 20 / (10 * 9)
= 20 / 90
= 2 / 9
So, the probability that both numbers drawn are odd is 2/9.