You have four cards, labeled 2-5. what is the probability of drawing a number less than 3, putting the card back, then drawing a prime number?

Step-by-step explanation:

Cards which are available are numbered as: {2, 3, 4, 5}

Number of cards available = 4

Selecting a number less than 3:

There is only one number less than 3, so only 1 way of selecting a card numbered less than 3. Therefore, the probability of selecting a card less than 3 =

Since this card is placed back, the total number of cards in the sample remain the same.

Selecting a prime number:

There are 3 prime numbers in the sample: 2,3 and 5

Probability of selecting a prime numbers would be 3 out 4 i.e. =

The two above mentioned events are independent of each other, so the probability of occurrence of both will be the product of their individual probabilities i.e.

Probability of drawing a number less than 3, putting the card back, then drawing a prime number =

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

∈3,600

step-by-step explanation: