Helena has a set of number cards numbered 1 through 10. If Helena randomly draws two cards from the deck, what is the probability that she will draw an odd number and then a two?
The answer i had was 1/18, but its not on there, so i need help and im confused.
I think it's 6/10
Hope this helps if it's not the answer let me know,
To find the probability of drawing an odd number first and then a two from a set of 1 to 10 number cards, we need to determine the total number of possible outcomes and the favorable outcomes.
Total Number of Possible Outcomes:
Since Helena draws two cards from a deck of 10, the total number of possible outcomes can be calculated using the concept of combinations. The number of combinations of n items taken r at a time is given by nCr, which stands for "n choose r." In this case, n = 10 (the total number of cards) and r = 2 (the number of cards drawn). So, the total number of possible outcomes is calculated as follows:
10C2 = (10!)/(2!(10-2)!) = 45
Favorable Outcomes:
To find the number of favorable outcomes, we need to consider the specific condition of drawing an odd number first and then a two.
Drawing an odd number first:
There are 5 odd numbers in the set of 1 to 10 (i.e., 1, 3, 5, 7, and 9). Helena will have a 5 out of 10 chance of drawing an odd number first.
Drawing a two next:
Since Helena has already drawn a card, there will be a total of 9 cards remaining (excluding the odd number drawn). Out of these 9 cards, only one is a two. Therefore, Helena will have a 1 out of 9 chance of drawing a two next.
To find the probability, multiply the probabilities of each step together:
Probability = (5/10) * (1/9) = 5/90
Simplify the fraction to its lowest terms:
Probability = 1/18
Therefore, the probability that Helena will draw an odd number first and then a two from the set of number cards is indeed 1/18.
odd numbers-1,3,5,7,9
even 2.4.6.8.10
prob odd then even= 5/10*5/9=25/90=5/18