Total Probability Theorem

Q. 18. Two whole numbers are randomly selected and multiplied . If the probability that the unit place in their product is even is P and the probability that the unit place in their product is odd is q then P/q is.

Q. 21. Ball is thrown from a urn containing 1 Red ball and 1 black ball. if the ball drawn is red a coin is tossed if it is black a dice thrown find the probability I) of each outcome II) getting head III) getting an even number

Q. 41. In a game called "odd man out", n(n>2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called odd man out. If the probability that there is a loser in any game is 1/2, then the value of n is

Q. The probabilities of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither A nor B happens is
(a) 0.39
(b) 0.25
(c) 0.11
(d) none of these

Q. An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :

1. $\frac{27}{49}$
2. $\frac{21}{49}$
3. $\frac{26}{49}$
4. $\frac{32}{49}$

Q. Consider four independent trials in which an event $A$ occurs with probability $\frac{1}{3}$. The event $B$ will occur with probability $1$ if the event $A$ occurs at least twice, it can not occur if the event $A$ does not occur and it occurs with a probability $\frac{1}{2}$ if the event $A$ occurs once. If the probability $p$ of the occurrence of event $B$ can be expressed as $\frac{m}{n},$ where $m,n\in N,$ then the least value of $m+n$ is

Q. Consider the following experiment :
$\text{Step 1.}$ Flip a fair coin twice.
$\text{Step 2.}$ If the outcomes are (TAILS, HEADS), then output $Y$ and stop.
$\text{Step 3.}$ If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop.
$\text{Step 4.}$ If the outcoms are (TAILS, TAILS), then go to $\text{Step 1.}$.

The probability that the output of the experiment is $Y$ is $\frac{1}{k}$. Then $k$ is

Q. 8. There are 7 red, 5 yellow and 3 blue balls in a box. From these, three balls were chosen randomly. Find the probability that the balls are not of the same color.

Q. A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?

Q. Two dice are thrown. Find the odds in favour of getting the sum (i) 4 (ii) 5.
(iii) What are the odds against getting the sum 6?

Q. two cards are drawn from a set of 52 cards .find the probability that atleast one of them wilk be an ace of hearts

Q. From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.