If the arrow is spun twice, what is the probability of getting
a, two 3s
b, two 4s
c,a 1 followed by a 2
d,a 4 followed by a 3
There are different ways to approach this problem, but one common method is to use the multiplication rule of probability, which states that the probability of two independent events both occurring is the product of their individual probabilities.
a) The probability of getting a 3 on a single spin is 1/6, since there are six equally likely outcomes. Assuming the spins are independent, the probability of getting two 3s in a row is the product of the probabilities of each spin: (1/6) x (1/6) = 1/36.
b) Similarly, the probability of getting a 4 on a single spin is 1/6, so the probability of two 4s in a row is (1/6) x (1/6) = 1/36.
c) To get a 1 followed by a 2, the arrow needs to land on 1 first and then on 2 on the second spin. The probability of getting a 1 on a single spin is 1/6, and assuming it happens, the probability of getting a 2 on the second spin is also 1/6. Therefore, the probability of getting a 1 followed by a 2 is (1/6) x (1/6) = 1/36.
d) To get a 4 followed by a 3, the arrow needs to land on 4 first and then on 3 on the second spin. The probability of getting a 4 on a single spin is 1/6, and assuming it happens, the probability of getting a 3 on the second spin is also 1/6. Therefore, the probability of getting a 4 followed by a 3 is (1/6) x (1/6) = 1/36.
To determine the probability of each event, we need to know the total number of possible outcomes and the number of favorable outcomes for each event.
Assuming the arrow is evenly divided into 6 sections numbered from 1 to 6 (as in a typical die), we have the following probabilities:
a) Two 3s:
To calculate the probability of getting two 3s, we need to determine how many favorable outcomes there are. With two spins of the arrow, the possible outcomes for each spin are 1, 2, 3, 4, 5, and 6. Since we are looking for two 3s, there is only one favorable outcome: (3, 3). Therefore, the probability of getting two 3s is 1 out of 36 possible outcomes, which can be simplified to 1/36.
b) Two 4s:
Similarly, the probability of getting two 4s is also 1 out of 36 possible outcomes, as there is only one favorable outcome: (4, 4). Therefore, the probability of getting two 4s is 1/36.
c) A 1 followed by a 2:
To calculate the probability of getting a 1 followed by a 2, we need to consider all possible outcomes. Since there is only one spin for the arrow that yields a 1, and one spin for the arrow that yields a 2, the probability of this event occurring is 1 out of 36 possible outcomes. Therefore, the probability of getting a 1 followed by a 2 is 1/36.
d) A 4 followed by a 3:
Similarly, the probability of getting a 4 followed by a 3 is 1 out of 36 possible outcomes, as there is only one favorable outcome: (4, 3). Therefore, the probability of getting a 4 followed by a 3 is 1/36.
In summary:
a) The probability of getting two 3s is 1/36.
b) The probability of getting two 4s is 1/36.
c) The probability of getting a 1 followed by a 2 is 1/36.
d) The probability of getting a 4 followed by a 3 is 1/36.