There are 6 cards numbered from 1 to 6. They are placed into a box, and then one is drawn and put back and then another card is drawn and put back. what is the probability that one of the cards was 5 if the sum of the two was 8?
This is the probability of drawing a 5 and a 3.
P(5) = 1/6
P(3) = 1/6
The probability of both/all events occurring is found by multiplying the individual events.
To determine the probability that one of the cards drawn was a 5, given that the sum of the two cards is 8, we first need to find the total number of possible outcomes and the number of favorable outcomes.
1. Total Number of Possible Outcomes:
Since there are 6 cards numbered from 1 to 6, each draw can result in any one of these 6 cards. Since two cards are drawn with replacement, there will be a total of 6 * 6 = 36 possible outcomes.
2. Number of Favorable Outcomes:
To calculate the number of favorable outcomes, we need to consider all the ways in which the sum of the two cards can be 8. Here are the combinations that satisfy this condition:
- 2 + 6 = 8
- 3 + 5 = 8
- 4 + 4 = 8
- 5 + 3 = 8
- 6 + 2 = 8
Among these combinations, two of them include a card with a 5: 3 + 5 = 8 and 5 + 3 = 8.
3. Calculating the Probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
So, the probability is 2 (favorable outcomes) / 36 (possible outcomes) = 1/18.
Therefore, the probability that one of the cards drawn was a 5, given that the sum of the two cards is 8, is 1/18.