Multiple Choice
A coin is tossed, and a standard number cube is rolled. What is the probability that the coin shows heads and the number cube shows an even number?
A. start fraction 1 over 6 end fraction
B. 1
C. one-fourth
D. one-half
D. one-half
A bag contains 3 blue marbles, 9 green marbles, and 11 yellow marbles. Twice you draw a marble and replace it. Find P(blue, then green).
A. 27/529
B. 27/23
C. 15/529
D. 12/23
The probability of drawing a blue marble on any one draw is 3/23, and the probability of drawing a green marble on any one draw is 9/23. Since we are replacing the marbles after each draw, the probability of drawing a blue marble and then a green marble is:
(3/23) * (9/23) = 27/529
Multiplying by 2 (since we are drawing twice) gives:
(27/529) * 2 = 54/529
Therefore, the answer is A. 27/529.
There are 9 candidates running for 3 seats on a committee. How many different election results are possible?
A. 36
B. 84
C. 504
D. 56
There are 9 candidates running for the first seat, then 8 candidates left for the second seat, and 7 candidates left for the third seat. However, the order in which the candidates are elected doesn't matter, so we need to divide by the number of ways of ordering the 3 elected candidates, which is 3! = 6. Therefore, the total number of different election results is:
(9 * 8 * 7) / 6 = 84
So the answer is B. 84.
To calculate the probability, we need to consider the outcomes of both the coin toss and the number cube roll.
The coin can show either heads or tails, which is a total of 2 possible outcomes.
The number cube can show any number from 1 to 6. However, we are only interested in the even numbers, which are 2, 4, and 6. Therefore, there are 3 possible outcomes for the number cube.
To find the probability of both events occurring, we multiply the probabilities of each event together.
The probability of getting heads on the coin is 1/2, and the probability of rolling an even number on the number cube is 3/6 (since 3 out of the 6 numbers are even).
Therefore, the probability of getting heads on the coin and an even number on the number cube is (1/2) * (3/6) = 3/12 = 1/4.
So, the correct answer is C. one-fourth.
To find the probability that the coin shows heads and the number cube shows an even number, we need to determine the number of favorable outcomes (the desired outcome) and the total number of possible outcomes.
1. For the coin toss:
- There are 2 possible outcomes (heads or tails).
- Since we want heads, there is 1 favorable outcome.
2. For the number cube roll:
- There are 6 possible outcomes (numbers 1 to 6).
- Since we want an even number, there are 3 favorable outcomes (2, 4, or 6).
To find the probability of both events happening, we multiply the probabilities of each event together:
P(coin shows heads) = 1/2
P(number cube shows an even number) = 3/6 = 1/2
P(coin shows heads and number cube shows an even number) = (1/2) * (1/2) = 1/4
Therefore, the correct choice is:
C. one-fourth