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
5 answers
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
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.
(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
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.
(9 * 8 * 7) / 6 = 84
So the answer is B. 84.