In roulette, a wheel with 38 numbers is spun. Of these, 18 are red, 18 are black, and 2 are green. The probability that when the wheel is spun it lands on any particular number is 1/38.
a) What is the probability that the wheel lands on a red number?
b) What is the probability that the wheel lands on a black number twice in a row?
c) What is the probability that the wheel lands on 0 or 00?
d) What is the probability that in five spins the wheel never lands on either 0 or 00?
e) What is the probability that the wheel lands on one of the first six integers on one spin, but does not land on any of them on the next spin?
I need to find how how to find the answers?
a) #red/total = ?
b) If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
c) Either-or probabilities are found by adding the individual probabilities.
d) (1-c)^5
e) 6/38 * (1-6/38) = ?
On a roulette wheel there are 38 sectors. Of these sectors, 18 are red, 18 are black , and 2 are green. When the wheel is spun, find the probability that the ball will land on
a) To find the probability that the wheel lands on a red number, we need to determine the number of red numbers out of the total numbers on the wheel and divide it by the total number of possibilities.
The number of red numbers is given as 18, and the total number of possibilities (numbers on the wheel) is given as 38.
So, the probability (P) of landing on a red number can be calculated as:
P(red) = Number of red numbers / Total number of possibilities
= 18 / 38
Simplifying the fraction, you get:
P(red) = 9 / 19
Therefore, the probability that the wheel lands on a red number is 9/19.
b) To find the probability that the wheel lands on a black number twice in a row, we need to multiply the probability of landing on a black number in one spin by itself since it needs to happen twice in a row.
The number of black numbers is given as 18, and the total number of possibilities (numbers on the wheel) is given as 38.
So, the probability (P) of landing on a black number in one spin can be calculated as:
P(black) = Number of black numbers / Total number of possibilities
= 18 / 38
To find the probability of landing on a black number twice in a row, we multiply this probability by itself:
P(black twice in a row) = P(black) * P(black)
= (18 / 38) * (18 / 38)
Simplifying the fraction and multiplying, you get:
P(black twice in a row) = 9 / 361
Therefore, the probability that the wheel lands on a black number twice in a row is 9/361.
c) To find the probability that the wheel lands on 0 or 00, we need to determine the number of 0s and 00s out of the total numbers on the wheel and divide it by the total number of possibilities.
The number of 0s and 00s is given as 2, and the total number of possibilities (numbers on the wheel) is given as 38.
So, the probability (P) of landing on 0 or 00 can be calculated as:
P(0 or 00) = Number of 0s and 00s / Total number of possibilities
= 2 / 38
Simplifying the fraction, you get:
P(0 or 00) = 1 / 19
Therefore, the probability that the wheel lands on 0 or 00 is 1/19.
d) To find the probability that in five spins, the wheel never lands on either 0 or 00, we need to calculate the probability of not landing on 0 or 00 for each spin and multiply them together.
The probability of not landing on 0 or 00 in one spin can be calculated as:
P(not 0 or 00) = 1 - P(0 or 00)
= 1 - (2 / 38)
Simplifying the fraction and subtracting, you get:
P(not 0 or 00) = 36 / 38
To find the probability of not landing on 0 or 00 in five spins, we multiply this probability by itself five times:
P(not 0 or 00 in five spins) = (36 / 38)^5
Calculating this equation, you get:
P(not 0 or 00 in five spins) ≈ 0.6216
Therefore, the probability that in five spins the wheel never lands on 0 or 00 is approximately 0.6216.
e) To find the probability that the wheel lands on one of the first six integers on one spin but does not land on any of them on the next spin, we need to find the probability of landing on one of the first six integers on the first spin and multiply it by the probability of not landing on any of them on the second spin.
The number of first six integers is given as 6, and the total number of possibilities (numbers on the wheel) is given as 38.
To calculate the probability of landing on one of the first six integers on one spin, we divide the number of first six integers by the total number of possibilities:
P(first six integers) = Number of first six integers / Total number of possibilities
= 6 / 38
The probability of not landing on any of the first six integers on the second spin is calculated as:
P(not first six integers) = 1 - P(first six integers)
= 1 - (6 / 38)
Simplifying the fraction and subtracting, you get:
P(not first six integers) = 32 / 38
To find the probability of landing on one of the first six integers on one spin but not landing on any of them on the next spin, we multiply these two probabilities together:
P(first six integers on one spin and not on the next) = P(first six integers) * P(not first six integers)
= (6 / 38) * (32 / 38)
Simplifying the fractions and multiplying, you get:
P(first six integers on one spin and not on the next) ≈ 0.0808
Therefore, the probability that the wheel lands on one of the first six integers on one spin but does not land on any of them on the next spin is approximately 0.0808.
To find the answers to these probability questions in roulette, you can use some basic principles of probability and counting.
a) The probability of landing on a red number can be calculated by dividing the number of red numbers (18) by the total number of numbers on the wheel (38). So, the probability of landing on a red number is 18/38.
b) The probability of landing on a black number twice in a row can be found by multiplying the probability of landing on a black number on one spin (18/38) with the probability of landing on a black number on the second spin (also 18/38). So, the probability is (18/38) * (18/38).
c) The probability of landing on 0 or 00 can be calculated by dividing the total number of green numbers (2) by the total number of numbers on the wheel (38). Hence, the probability is 2/38.
d) The probability of the wheel not landing on either 0 or 00 in five consecutive spins can be calculated by finding the probability of not landing on 0 or 00 on one spin (36/38), and then multiplying this probability by itself for five consecutive spins. So, the probability is (36/38)^5.
e) The probability of the wheel landing on one of the first six integers on one spin and not landing on any of them on the next spin can be calculated by dividing the number of favorable outcomes (6 integers on the first spin and 32 non-integers on the second spin) by the total number of outcomes on the wheel (38). So, the probability is (6/38) * (32/38).
By using these calculations, you can determine the probabilities for each of the given scenarios in roulette.