There are 5 lemon sweets and 4 orange sweets in a bag, susan takes one out randomly and eats it then ann takes one out at random. calculate the probability that they both take out a sweet of the same flavour.
Is there 3 possible outcomes. I am really stuck trying to work this out, can someone give advice please how to calculate.
susan takes lemon then ann takes lemon:
5/9 * 4/8 = 20/72 = 5/13
susan takes orange then ann takes orange:
4/9 * 3/8 = 1/6
add them
Well, it seems like Susan and Ann have quite the sweet tooth! Let's break it down step by step.
First, let's look at Susan's turn. Since there are a total of 9 sweets in the bag (5 lemon + 4 orange), the probability of Susan picking a lemon sweet is 5/9, and the probability of her picking an orange sweet is 4/9.
Now, let's move on to Ann's turn. After Susan picks a sweet, there will be 8 sweets left in the bag. If Susan picked a lemon, there will be 4 lemon sweets and 4 orange sweets left, giving Ann a 4/8 (or simplified to 1/2) chance of picking a lemon sweet. If Susan picked an orange, there will be 5 lemon sweets and 3 orange sweets left, giving Ann a 5/8 chance of picking a lemon sweet.
Finally, to calculate the probability that both Susan and Ann pick a sweet of the same flavor, we can multiply their individual probabilities together. So, if Susan picks a lemon (probability of 5/9) and then Ann picks a lemon (probability of 1/2), the overall probability would be (5/9) * (1/2) = 5/18.
Similarly, if Susan picks an orange (probability of 4/9), and then Ann picks an orange (probability of 3/8), the overall probability would be (4/9) * (3/8) = 12/72, which can be simplified to 1/6.
Now, to obtain the total probability, we can add up the probabilities of both scenarios: (5/18) + (1/6) = 5/18 + 3/18 = 8/18.
Therefore, the probability that Susan and Ann both pick a sweet of the same flavor is 8/18, which can be simplified to 4/9 or approximately 0.444.
I hope this explanation didn't leave you feeling sour!
Only one possible outcome.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P (Both lemon) = 5/9 * (5-1)/(9-1) = ?
P (both orange) = 4/9 * 3/8 = ?
Either-or probabilities are found by adding the individual probabilities.
P(both lemon) + P(both orange) = ?
5/9 * 4/8 = 20/72 = 5/18
Thanks to both Damon and PsyDAG for helping me get round this problem. I think I was making it too complicated.
Welcome
To calculate the probability that Susan and Ann both take out a sweet of the same flavor, you need to determine the total number of possible outcomes and the number of favorable outcomes.
1. Total Number of Possible Outcomes:
The total number of possible outcomes is the product of the number of options for Susan and Ann. In this case, there are 5 lemon sweets and 4 orange sweets, so Susan has 9 options and Ann has 8 options. Therefore, the total number of possible outcomes is 9 x 8 = 72.
2. Number of Favorable Outcomes:
The number of favorable outcomes is the number of instances where both Susan and Ann pick a sweet of the same flavor. There are two possibilities for this: they both pick a lemon or they both pick an orange.
- If Susan picks a lemon, there are 5 lemon sweets remaining and 3 orange sweets. Therefore, Ann has a 5/8 chance of picking a lemon.
- If Susan picks an orange, there are 4 orange sweets remaining and 4 lemon sweets. Therefore, Ann has a 4/8 chance of picking an orange.
To calculate the number of favorable outcomes, you multiply these probabilities:
(5/9) x (4/8) = 20/72
3. Calculating the Probability:
Finally, to calculate the probability, divide the number of favorable outcomes by the total number of possible outcomes:
(20/72) = 5/18
Therefore, the probability that both Susan and Ann pick a sweet of the same flavor is 5/18 or approximately 0.278, which means there is a 27.8% chance they will both pick a sweet of the same flavor.