Desirable vs Favourable Outcome

Q. Can the number of favourable outcomes ever exceed the total number of outcomes?

1. Yes
2. No

Q. In a game, we roll a fair die. If we roll an odd number, we lose and we win if we roll an even number. We are interested in computing the probability of losing this game. Which of the following is the desired outcome and the favorable outcome respectively?

1. $P\left(Winning\right)$, $P\left(Losing\right)$
2. $P\left(Losing\right)$, $P\left(Winning\right)$
3. $P\left(Losing\right)$, $P\left(Losing\right)$
4. $P\left(Winning\right)$, $P\left(Winning\right)$

Q. A favourable outcome is an event whose probability we are interested in computing or the outcome of interest.

1. True
2. False

Q. In any given experiment, the set of desired outcomes that we are interested in is knows as the favourable outcomes.

1. True
2. False

Q. For the given situation,


find the probability of getting an even number when an unbiased die is rolled.

Also, find the desirable outcome in this case.

1. $P\left(E\right)=\frac{1}{2}$
   Desired outcome $=$ Getting an odd number
2. $P\left(E\right)=\frac{1}{2}$
   Desired outcome $=$ Getting an even number

Q. For the given situation,


find the probability of getting an odd number when a die is rolled.

Also, check whether desired outcome is same as favorable outcome.

1. $\text{P(O)}=\frac{1}{2}$
   
   The desired outcome is same as favorable outcome, i.e., Getting an odd number.
2. $\text{P(O)}=\frac{1}{2}$
   
   The desired outcome is not the same as favorable outcome, i.e., Getting an odd number.
3. $\text{P(O)}=\frac{1}{2}$
   
   The desired outcome is same as favorable outcome, i.e., Getting an even number.
4. $\text{P(O)}=\frac{1}{2}$
   
   The desired outcome is not the same as favorable outcome, i.e., Getting an even number.

Q. A coin is tossed and a die is rolled one after the other. Find the probability of flipping a tail and seeing a 4.

1. $\frac{1}{2}$
2. $\frac{1}{12}$
3. $\frac{1}{6}$

Q. A fair die is rolled and a number divisible by 3 shows up. The set of favourable outcomes when this event occurs is

1. $\{2,3,6\}$
2. $\{3,6\}$
3. $\{3,6,9)$

Q.

Choose whether the outcomes are impossible, unlikely, even chance, likely, or certain:

The number on the top face of an ordinary dice when rolled will be more than will be more than 6.

Q. Desirable outcome is always the same as the favorable outcome.

1. True
2. False