A six sided die is tossed. What is the probability that it shows a prime number if you know the following?

a. It shows an even number.
b. It shows a number less than 5.
c. It does not show a 6.
d. It shows 1 or 2/
e. It shows an even number less than 4.
f. It shows a number greater than 3.

a) the only even prime is the number 2 so

prob = 1/6

b) primes less than 5 are : 2 and 3
so prob = 2/6 = 1/3

c) if not a 6, then it must be: 1, 2, 3, 4, or 5
how many of those are prime?

d) which of 1 or 2 is prime ?

e) how many even's < 4 are prime?

etc.

To find the probabilities, we first need to determine the favorable outcomes (the favorable outcomes are the numbers that satisfy the condition) and the total possible outcomes (the total number of outcomes from rolling a six-sided die).

a. If it shows an even number (2, 4, or 6), there are three favorable outcomes: 2, 4.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 3/6 or 1/2.

b. If it shows a number less than 5 (1, 2, 3, or 4), there are four favorable outcomes: 2, 3, 4.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 4/6 or 2/3.

c. If it does not show a 6, there are five favorable outcomes: 1, 2, 3, 4, 5.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 5/6.

d. If it shows 1 or 2, there are two favorable outcomes: 2.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 2/6 or 1/3.

e. If it shows an even number less than 4 (2), there is one favorable outcome: 2.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 1/6.

f. If it shows a number greater than 3 (4, 5, or 6), there are three favorable outcomes: 4, 5, 6.
The total possible outcomes are six (1, 2, 3, 4, 5, 6).

Therefore, the probability is 3/6 or 1/2.

Note: Prime numbers are numbers that are only divisible by 1 and themselves. In the case of the six-sided die, the prime numbers are 2, 3, and 5.