6. A spinner has 3 equal sections: red, white, and blue. John spins the spinner and tosses a coin. Which shows the sample space for spinning the spinner and tossing the coin? (1 point)%0D%0A%09%0D%0A %09 Red%09 White%09 Blue%0D%0A Heads%09 Heads, Red%09 Heads, White%09 Heads, Blue%0D%0A Tails%09 Heads, Red%09 Heads, White%09 Heads, Blue%0D%0A%09%0D%0A %09 Red%09 White%0D%0A Heads%09 Heads, Red%09 Heads, White%0D%0A Tails%09 Heads, Red%09 Heads, White%0D%0A%09%0D%0A %09 Red%09 White%09 Blue%0D%0A Heads%09 Heads, Red%09 Heads, White%09 Heads, Blue%0D%0A%09%0D%0A %09 Red%09 White%09 Blue%0D%0A Heads%09 Heads, Red%09 Heads, White%09 Heads, Blue%0D%0A Tails%09 Tails, Red%09 Tails, White%09 Tails, Blue
8. The probability it will snow in the next two weeks is for this week and for next week. What is P(snow this week, then snow next week)? (1 point)
11. Ariel wants to choose 5 players for her basketball team. There are 7 players to choose from. How many different teams can Ariel make? (1 point)%0D%0A%0921%0D%0A%0935%0D%0A%0942%0D%0A%0956
16. There are 20 entries in the chess tournament. How many ways can they finish in first, second, and third place? (1 point)%0D%0A%09340%0D%0A%096,840%0D%0A%097,220%0D%0A%098,350
17. A bag contains tiles with the letters C-O-M-B-I-N-A-T-I-O-N-S. Lee chooses a tile without looking and doesn’t replace it. He chooses a second tile without looking. What is the probability that he will choose the letter O both times? (1 point)
18. An ice cream shop offers the toppings shown below. How many 4-topping ice cream sundaes can you make?%0D%0A%0D%0Achocolate chips%0D%0Awalnuts%0D%0Astrawberry sprinkles%0D%0Acaramel%0D%0Ahot fudge%0D%0Awhipped cream%0D%0Agummy bears (1 point)%0D%0A%0911%0D%0A%0928%0D%0A%0930%0D%0A%0935%0D%0AFinishCancel
6. The sample space for spinning the spinner and tossing the coin is:
- Red, Heads
- Red, Tails
- White, Heads
- White, Tails
- Blue, Heads
- Blue, Tails
Answer: Option C
8. The probability of snow this week and next week is:
P(snow this week, then snow next week) = P(snow this week) x P(snow next week)
= x
=
Answer:
11. The number of different teams Ariel can make is given by selecting 5 players out of 7, which is
Answer: Option A
16. The number of ways the chess tournament can finish in first, second, and third place is given by the permutation formula P(20,3) which is
Answer: Option D
17. The probability of choosing the letter O both times is the product of the probability of choosing O in the first draw (which is 2/13, since there are 2 O's in the bag of 13 tiles) and the probability of choosing O in the second draw given that the first draw was O (which is 1/12, since there would be 1 O left in a bag of 12 tiles after the first O was drawn). So the total probability is
Answer: Option C
18. The number of 4-topping ice cream sundaes we can make is the number of ways we can select 4 toppings out of 7, which is
Answer: Option B
is no.8 1/48?
No, the answer for no.8 is:
P(snow this week, then snow next week) = P(snow this week) x P(snow next week)
= x
=
Without knowing the actual values of P(snow this week) and P(snow next week), we cannot calculate the answer.
8. The probability it will snow in the next two weeks is 1/12 for this week and 1/4 for next week. What is P(snow this week, then snow next week)? (1 point)
Using the given probabilities, we can calculate the probability of snow this week and next week as follows:
P(snow this week, then snow next week) = P(snow this week) x P(snow next week)
= (1/12) x (1/4)
= 1/48
So the answer is 1/48.
6. The sample space for spinning the spinner and tossing the coin can be determined by listing all the possible outcomes. We have 3 options for the spinner (red, white, and blue) and 2 options for the coin (heads and tails). To find the total number of outcomes, we multiply the number of options for the spinner by the number of options for the coin.
The sample space for spinning the spinner and tossing the coin is:
Red, Heads
Red, Tails
White, Heads
White, Tails
Blue, Heads
Blue, Tails
So the answer is: Red, Heads, Red, Tails, White, Heads, White, Tails, Blue, Heads, Blue, Tails.
8. To find the probability that it will snow this week and next week, we multiply the probability of snow this week by the probability of snow next week.
Let's say the probability of snow this week is p1 and the probability of snow next week is p2.
P(snow this week, then snow next week) = p1 * p2
11. To find the number of different teams Ariel can make, we need to use the concept of combinations. The number of ways to choose 5 players out of 7 can be calculated using the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of players and r is the number of players to be chosen.
In this case, n = 7 and r = 5.
Number of different teams = 7C5 = 7! / (5!(7-5)!) = 7! / (5!2!) = (7 * 6 * 5!) / (5! * 2 * 1) = (7 * 6) / (2 * 1) = 7 * 3 = 21
So Ariel can make 21 different teams.
16. To find the number of ways the 20 entries in the chess tournament can finish in first, second, and third place, we need to consider the concept of permutations. The number of ways to arrange the entries in the top 3 positions can be calculated using the formula for permutations, which is nPr = n! / (n-r)!, where n is the total number of entries and r is the number of positions to be filled.
In this case, n = 20 and r = 3.
Number of ways to finish in first, second, and third place = 20P3 = 20! / (20-3)! = 20! / 17! = 20 * 19 * 18 = 6,840
So there are 6,840 ways the entries can finish in first, second, and third place.
17. The probability that Lee will choose the letter O both times can be calculated by dividing the number of favorable outcomes (choosing the letter O twice) by the total number of possible outcomes.
There are 3 O's in the word "COMBINATIONS" out of a total of 12 letters. When Lee chooses without replacement, the number of O's decreases to 2, and the total number of letters decreases to 11.
The probability of choosing the letter O the first time is 3/12, and the probability of choosing the letter O the second time (without replacement) is 2/11.
Therefore, the probability of choosing the letter O both times is (3/12) * (2/11) = 6/132 = 1/22.
18. To calculate the number of 4-topping ice cream sundaes we can make, we need to use the concept of combinations. Since the order of toppings doesn't matter for the sundae, we need to calculate the combinations of 4 toppings chosen from the given list.
The number of ways to choose 4 toppings out of 7 can be calculated using the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of toppings and r is the number of toppings to be chosen.
In this case, n = 7 and r = 4.
Number of 4-topping ice cream sundaes = 7C4 = 7! / (4!(7-4)!) = 7! / (4! * 3!) = (7 * 6 * 5 * 4!) / (4! * 3 * 2 * 1) = 7 * 6 * 5 / (3 * 2 * 1) = 35
So we can make 35 different 4-topping ice cream sundaes.