I am stuck on several probability questions.
A spinner that has 15 equal sized sections numbered 1 to 15 is spun twice. What is the probability the spinner lands on an odd number and then on an even number? A. 56/225 B. 169/225 C. 1/15 D. 21/225 I chose A. 56/225 because 8/15 x 7/15 = 56/225.
Is this correct?
A bag contains 9 metal balls, 10 hollow balls, 4 glass balls and 18 plastic balls. What is the probability of choosing a glass or hollow ball? A. 24.6% B. 38.9% C. 35.4% D. 34.1%
What is the probability of receiving a 6 or a 9 from a deck of 52 cards and an ace or a King? A. 1.7% B. 15% C. 2.4% D. 5.6%
Yes, your answer for the first question is correct.
To calculate the probability of landing on an odd number and then an even number, we multiply the probabilities of each event.
There are 8 odd numbers (1, 3, 5, 7, 9, 11, 13, 15) out of 15 total numbers on the spinner, so the probability of landing on an odd number on the first spin is 8/15.
After spinning an odd number, there are 7 even numbers (2, 4, 6, 8, 10, 12, 14) left out of the remaining 14 numbers, so the probability of landing on an even number on the second spin is 7/14 (or simplified, 1/2).
Multiplying these probabilities gives us (8/15) * (7/14) = 56/225, which matches option A.
Now, let's solve the other two probability questions.
For the second question, the total number of balls in the bag is 9 + 10 + 4 + 18 = 41. The number of glass and hollow balls is 10 + 4 = 14.
So, the probability of choosing a glass or hollow ball is 14/41. Converting this to a percentage gives us approximately 34.1%, which matches option D.
For the third question, we need to find the probability of receiving a 6 or a 9 from the deck of 52 cards and an ace or a King.
There are four 6s and four 9s in a deck of 52 cards, so the probability of receiving a 6 or a 9 is 8/52 (or simplified, 2/13).
There are four aces and four kings in a deck of 52 cards, so the probability of receiving an ace or a king is 8/52 (or simplified, 2/13).
Since these events are independent, we can simply add these probabilities: (2/13) + (2/13) = 4/13.
Converting this to a percentage gives us approximately 30.8%, which is not one of the given options. Therefore, none of the given options match the correct answer.
Question 1:
To find the probability of two independent events occurring, we multiply their individual probabilities. In this case, we need to find the probability of spinning an odd number first and then spinning an even number.
The probability of spinning an odd number on the first spin is given by the number of odd numbers (8) divided by the total number of possible outcomes (15), which is 8/15.
On the second spin, since one odd number has been removed from the spinner, we have 7 odd numbers left. Therefore, the probability of spinning an even number is 7/15.
To find the probability of both events occurring, we multiply these probabilities together:
(8/15) x (7/15) = 56/225
So you are correct, the probability is A. 56/225.
Question 2:
In this question, we need to find the probability of choosing a glass ball or a hollow ball from the given options.
The total number of balls in the bag is 9 + 10 + 4 + 18 = 41.
The number of glass balls is 4, and the number of hollow balls is 10. So, the number of balls that are either glass or hollow is 4 + 10 = 14.
Thus, the probability of choosing a glass or hollow ball is given by the number of favorable outcomes (14) divided by the total number of possible outcomes (41):
14/41 ≈ 0.341
In percentage form, this is approximately 34.1%. So the correct answer is D. 34.1%.
Question 3:
To find the probability of receiving a 6 or a 9 from a deck of 52 cards and an ace or a King, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
The number of 6s and 9s in a deck of cards is 4 (two 6s and two 9s). The number of aces and kings is also 4 (one ace and three kings).
Therefore, the number of favorable outcomes is 4 + 4 = 8.
The total number of cards in a deck is 52.
So, the probability is given by the number of favorable outcomes (8) divided by the total number of possible outcomes (52):
8/52 = 2/13 ≈ 0.154.
In percentage form, this is approximately 15%. Therefore, the correct answer is B. 15%.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
8/15 * 7/15 = ?
Either-or probabilities are found by adding the individual probabilities.
4/41 + 10/41 = ?
With replacement, 6 or 9 = 8/52 and Ace or King = 8/52.
Without replacement, 6 or 9 = 8/52 and Ace or King = 8/51.
Again, if the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Yes
D
I don't know sorry