You roll a number cube twice. find the probability of the events. 1.rolling a 3 twice 2.rolling an even number and a 5 3.rolling an odd number and a 2 or 4 4.rolling a number less than 6 and a 3 or a 1

In a number cube, a dice, you have six sides with the numbers 1, 2, 3, 4, 5 and 6. And when you roll it, each number has the same probability of showing.

a) rolling a 3 twice.

In the first roll you get a 3, with a probability of 1/6, and with the second roll you also get a 3, also with a probability of 1/6. The probability of bot evets to happen is equal to the product of the individual probabilities.

P = 1/6*1/6 = 1/36

b) An even number and a 5.

In the first roll you can get 2, 4 or 6, so you have 3 out of 6 options, the probability is 3/6 = 1/2, in the second roll you need you get a 5, the probability is 1/6.

P = 1/2*1/6 = 1/12.

But we also have the probability where the first dice is a 5 and the second a pair number, so the real probability is 2*P = 1/6

c) an odd number and 2 or 4.

for an odd number the probability is 3/6 = 1/2, for getting 2 or 4 the probability is 2/6 = 1/3

then we have that P = 2*(1/3)*(1/2) = 1/3

d) a number less than 6, you have 5 options, then the probability is:

p = 5/6, and for 3 or 1 the probability is 2/6 = 1/3

then P = 2*(5/6)*(1/3) = 5/9

the answer to this question is yes