Ha!These are all from AoPS. Anyways,
1) probability of green then red = p(green) * p(red). Take a common multiple of 13 & 5 that's under 100 - I chose 65. The numerators all have to add up to the denominator in the probability. p(red) = 15/65. p(blue) = 26/65. so p(green) has to equal (65 - (15+26))/65 = 24/65. Using cross multiplication, you can find out that 24/65 * 15/65 = 9/104.
Hi! I'm Maddie. I need some help on my homework. Here are three problems I need help with:
A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability of selecting a blue marble from the bowl is 2/5. There are fewer than 100 marbles in the bowl. What is the probability of selecting, at random and without replacement, a green marble and then a red marble from the bowl on the first two selections? Express your answer as a common fraction.
The second one is:
The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the resulting number is divisible by 4? Express your answer as a common fraction.
And the last one is:
A six-sided die (with numbers 1 through 6) and an eight-sided die (with numbers 1 through 8) are rolled. What is the probability that there is exactly one 6 showing? Express your answer as a common fraction.
Thank you so much if you can help!! It would be amazing if you could help me out.
4 answers
2) A number is divisible by 4 if and only if the number formed by its last two digits is divisible by 4. Using the given digits, we find that the only two-digit numbers that are divisible by 4 are 24, 28, 32, 48, 72, and 84.
The probability that the number is divisible by 4 is the number of last-2-digit combinations that make it divisible by four divided by the total ways to choose the last 2 digits.
There are 4 * 5 = 20 ways to choose the last two digits, and they are all equally likely, so the probability that the number is divisible by 4 is 6/20 = 3/10.
The probability that the number is divisible by 4 is the number of last-2-digit combinations that make it divisible by four divided by the total ways to choose the last 2 digits.
There are 4 * 5 = 20 ways to choose the last two digits, and they are all equally likely, so the probability that the number is divisible by 4 is 6/20 = 3/10.
3) If there is exactly one 6 showing, then the 6 must be on the six-sided die or the eight-sided die (but not both).
The probability of getting a 6 with the six-sided die is 1/6, and the probability of not rolling a 6 with the eight-sided die is 7/8.
The probability of not getting a 6 with the six-sided die is 5/6, and the probability of rolling a 6 with the eight-sided die is 1/8.
Therefore, the probability that there is exactly one 6 is 1/6 * 7/8 + 5/6 * 1/8 = 7/48 + 5/48 = 12/48 = 1/4
The probability of getting a 6 with the six-sided die is 1/6, and the probability of not rolling a 6 with the eight-sided die is 7/8.
The probability of not getting a 6 with the six-sided die is 5/6, and the probability of rolling a 6 with the eight-sided die is 1/8.
Therefore, the probability that there is exactly one 6 is 1/6 * 7/8 + 5/6 * 1/8 = 7/48 + 5/48 = 12/48 = 1/4
So your answers are:
1) 9/104
2) 3/10
3) 1/4
1) 9/104
2) 3/10
3) 1/4
1 answer