QuestionFind the probabilities of selecting marble 2 first and marble 5 second from a bag with an unknown number of marbles.

Studdy Solution

STEP 1

Assumptions1. The total number of marbles in the bag is not specified, but it is at least5 (as we have marbles numbered and5). . Each marble in the bag is distinct and numbered.
3. The selection of a marble is a random process.
4. After a marble is selected, it is put back into the bag and the marbles are mixed before the next selection.
5. Events A and B are independent, meaning the outcome of the first selection does not affect the outcome of the second selection.

STEP 2

We need to determine the probabilities associated with Events A and B.The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the total number of outcomes is the total number of marbles in the bag, which is unspecified.Let's denote the total number of marbles as 'n'.
The probability of Event A (the first selection is marble number2) is then $(A) = \frac{1}{n}$

STEP 3

Similarly, the probability of Event B (the second selection is marble number5) is also $(B) = \frac{1}{n}$

STEP 4

Since Events A and B are independent, the probability of both events occurring is the product of their individual probabilities. Therefore, the probability of both Event A and Event B occurring is $(A \cap B) =(A) \times(B)$

STEP 5

Substitute the values of(A) and(B) into the equation from4 $(A \cap B) = \frac{1}{n} \times \frac{1}{n}$

STEP 6

implify the equation to get the final probability $(A \cap B) = \frac{1}{n^2}$ So, the probability of selecting marble number2 first and then marble number5 is1 divided by the square of the total number of marbles in the bag.

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QuestionFind the probabilities of selecting marble 2 first and marble 5 second from a bag with an unknown number of marbles.

Studdy Solution

STEP 1

STEP 2

STEP 3

Similarly, the probability of Event B (the second selection is marble number5) is also $(B) = \frac{1}{n}$

STEP 4

Since Events A and B are independent, the probability of both events occurring is the product of their individual probabilities. Therefore, the probability of both Event A and Event B occurring is $(A \cap B) =(A) \times(B)$

STEP 5

Substitute the values of(A) and(B) into the equation from4 $(A \cap B) = \frac{1}{n} \times \frac{1}{n}$

STEP 6

implify the equation to get the final probability $(A \cap B) = \frac{1}{n^2}$ So, the probability of selecting marble number2 first and then marble number5 is1 divided by the square of the total number of marbles in the bag.

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QuestionFind the probabilities of selecting marble 2 first and marble 5 second from a bag with an unknown number of marbles.

Studdy Solution

STEP 1

STEP 2

STEP 3

Similarly, the probability of Event B (the second selection is marble number5) is also(B)=1n(B) = \frac{1}{n}(B)=n1​

STEP 4

Since Events A and B are independent, the probability of both events occurring is the product of their individual probabilities. Therefore, the probability of both Event A and Event B occurring is(A∩B)=(A)×(B)(A \cap B) =(A) \times(B)(A∩B)=(A)×(B)

STEP 5

Substitute the values of(A) and(B) into the equation from4(A∩B)=1n×1n(A \cap B) = \frac{1}{n} \times \frac{1}{n}(A∩B)=n1​×n1​

STEP 6

implify the equation to get the final probability(A∩B)=1n2(A \cap B) = \frac{1}{n^2}(A∩B)=n21​So, the probability of selecting marble number2 first and then marble number5 is1 divided by the square of the total number of marbles in the bag.

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Similarly, the probability of Event B (the second selection is marble number5) is also $(B) = \frac{1}{n}$

Since Events A and B are independent, the probability of both events occurring is the product of their individual probabilities. Therefore, the probability of both Event A and Event B occurring is $(A \cap B) =(A) \times(B)$

Substitute the values of(A) and(B) into the equation from4 $(A \cap B) = \frac{1}{n} \times \frac{1}{n}$

implify the equation to get the final probability $(A \cap B) = \frac{1}{n^2}$ So, the probability of selecting marble number2 first and then marble number5 is1 divided by the square of the total number of marbles in the bag.