How do i solve these?
1) Two dice are thrown simultaneously. The probability that the
product of the two numbers on the two dice is an even number?
2) A bag contains red and blue marbles totaling between 50 to 100 in number. If two marbles are drawn at random, the chances of them both being red are 25%. One third of the marbles are picked from the bag and thrown away. If one marble is now drawn at random from the bag, what is the probability of it being blue? (Answer in %)
3) What is the probability that the product of two consecutive non-negative integers will be a number ending with 0?
---- My workings:
For the 1st problem, this is what i did:
The possible even values on rolling a pair of dice will be 18. So, im getting an incorrect answer of 18/36 (1/2). The source reports 3/4
For the 2nd one:
I assumed the set of marbles to be 6, since the answer is supposed to be in % and the 50 to 100 range seems absurd. So, 25% of 6 will be 2 red marbles. Rest are 4 blue marbles. 1/3rd of the total set is removed randomly which makes it obvious that two blue marbles were the ones removed. So, my answer sums up to 50% of blue balls. The answer is correct but am not sure of my logic.
For the 3rd one:
I considered the range from 0-9. So, the consecutive numbers ending with 0 are 3 out of 10. So, i am getting 3/10 which is incorrect.