Tamara likes to mix and match her 4 scarves, 3 pairs of gloves, and 2 hats. The colors are in the table. On Monday, she randomly picks out a scarf, hat, and a pair of gloves. What is the probability of Tamara choosing a pair of brown gloves and a red hat?
A three column table is shown. The first column is titled 'Scarf' and contains 'Red,' 'White,' 'Brown,' and 'Black.' The second column is titled 'Gloves' and contains 'Black,' 'Brown,' and 'Red.' The third column is titled 'Hat' and contains 'White' and 'Red.'
(1 point)
one-fourth
one-eighth
one-tenth
start fraction 1 over 6 end fraction
The probability of Tamara picking a brown pair of gloves is 1/3, and the probability of her picking a red hat is 1/2. Since she can choose any scarf, there is a total of 4 options for the scarf. Therefore, the probability of her choosing a brown pair of gloves and a red hat with any scarf is:
1/3 (probability of brown gloves) x 1/2 (probability of red hat) x 4 (number of scarf options)
= 2/12
= 1/6
Therefore, the probability of Tamara choosing a pair of brown gloves and a red hat is 1/6 or start fraction 1 over 6 end fraction. The answer is (d) one-sixth.
. Which events are not independent? (1 point)
You toss three coins and get one head and one tail.
You choose three different ice toppings for a sundae.
You draw two colored pencils without replacement and get one red and one yellow.
You pull a yellow marble from a bag of marbles, return it, and then pull a green marble
The events of drawing a yellow marble and then drawing a green marble from a bag of marbles are not independent, as the first draw affects the probability of the second draw. The other events listed are independent.
A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? (1 point)
start fraction 1 over 6 end fraction
start fraction 1 over 12 end fraction
start fraction 2 over 3 end fraction
one-fourth
The probability of flipping heads on a coin is 1/2. The probability of rolling 5 on a number cube is 1/6. To find the probability of both events occurring, we multiply the individual probabilities:
1/2 x 1/6
= 1/12
Therefore, the probability that the coin shows heads and the number cube shows 5 is start fraction 1 over 12 end fraction. The answer is (b) start fraction 1 over 12 end fraction.
15. On Friday nights the local diner serves three main entrées, each with a choice of vegetable. The entrées are beef, chicken, and fish. The vegetables are spinach, broccoli, and carrots. How many possible dinners (entrée and vegetable combinations) does the diner serve? List them.
There are 3 choices of entrées (beef, chicken, or fish) and 3 choices of vegetables (spinach, broccoli, or carrots). To find the total number of possible dinner combinations, we multiply the number of entrée choices by the number of vegetable choices:
3 x 3
= 9
Therefore, the diner serves 9 possible dinner combinations:
1. Beef with spinach
2. Beef with broccoli
3. Beef with carrots
4. Chicken with spinach
5. Chicken with broccoli
6. Chicken with carrots
7. Fish with spinach
8. Fish with broccoli
9. Fish with carrots