Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and Ek={(a,b)∈S:ab=k}. If Pk=P(Ek), then the correct among the following is
- p1<p10<p4
- p2<p8<p14
- p4<p8<p17
- p1<p10<p4
The Correct Option is A
Solution and Explanation
The sample space, denoted as S, consists of all possible outcomes when rolling two six-sided dice. Each outcome is represented as (x, y), where x and y can take values from 1 to 6. Therefore, the sample space S includes (1,1), (1,2), ..., (1,6), (2,1), ..., (2,6), ..., (6,1), ..., and (6,6).
The total number of elements in the sample space is calculated as 6^2, which equals 36.
The probability of getting the specific outcome (1,1) is 1 out of the total number of elements in the sample space, which is 36.
So, p(1,1) = 1/36.
The correct answer is option (A): p1<p10<p4
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Concepts Used:
Probability
Probability is defined as the extent to which an event is likely to happen. It is measured by the ratio of the favorable outcome to the total number of possible outcomes.
The definitions of some important terms related to probability are given below:
Sample space
The set of possible results or outcomes in a trial is referred to as the sample space. For instance, when we flip a coin, the possible outcomes are heads or tails. On the other hand, when we roll a single die, the possible outcomes are 1, 2, 3, 4, 5, 6.
Sample point
In a sample space, a sample point is one of the possible results. For instance, when using a deck of cards, as an outcome, a sample point would be the ace of spades or the queen of hearts.
Experiment
When the results of a series of actions are always uncertain, this is referred to as a trial or an experiment. For Instance, choosing a card from a deck, tossing a coin, or rolling a die, the results are uncertain.
Event
An event is a single outcome that happens as a result of a trial or experiment. For instance, getting a three on a die or an eight of clubs when selecting a card from a deck are happenings of certain events.
Outcome
A possible outcome of a trial or experiment is referred to as a result of an outcome. For instance, tossing a coin could result in heads or tails. Here the possible outcomes are heads or tails. While the possible outcomes of dice thrown are 1, 2, 3, 4, 5, or 6.