A die is thrown, find the probability of the following events:(i) A prime number will appear,(ii) A number greater than or equal to \(3\) will appear,(iii) A number less than or equal to one will appear,(iv) A number more than \(6\) will appear,(v) A number less than 6 will appear.
A die is thrown, find the probability of the following events:(i) A prime number will appear,(ii) A number greater than or equal to \(3\) will appear,(iii) A number less than or equal to one will appear,(iv) A number more than \(6\) will appear,(v) A number less than 6 will appear.
Solution and Explanation
A die is thrown, find the probability of the following events:
(i) A prime number will appear,
(ii) A number greater than or equal to \(3\) will appear,
(iii) A number less than or equal to one will appear,
(iv) A number more than 6 will appear,
(v) A number less than 6 will appear.
The sample space of the given experiment is given by
\(S = \{1, 2, 3, 4, 5, 6\}\)
(i) Let \(A\)\(\) be the event of the occurrence of a prime number.
Accordingly, \(A = \{2, 3, 5\}\)
∴\(∴P(A)=\dfrac{\text{Number } \text{of }\text{ outcomes }\text{ favorable} \text{ to }A}{\text{Total } \text{number }\text{ of}\text{ possible }\text{outcomes }}\)
\(=\dfrac{n(A)}{n(S)}\)
\(=\dfrac{3}{6}\)
\(=\dfrac{1}{2}\)
(ii) Let \(B\) be the event of the occurrence of a number greater than or equal to \(3.\) Accordingly, \(B = \{3, 4, 5, 6\}\)
\(∴P(B)=\dfrac{\text{Number } \text{of }\text{ outcomes }\text{ favorable} \text{ to }B}{\text{Total } \text{number }\text{ of}\text{ possible }\text{outcomes }}\)
\(=\dfrac{n(A)}{n(S)}\)
\(=\dfrac{4}{6}\)
\(=\dfrac{2}{3}\)
(iii) Let \(C\) be the event of the occurrence of a number less than or equal to one. Accordingly, \(C = \{1\} \)
\(∴P(C)=\dfrac{\text{Number } \text{of }\text{ outcomes }\text{ favorable} \text{ to }C}{\text{Total } \text{number }\text{ of}\text{ possible }\text{outcomes }}\)
\(=\dfrac{n(C)}{n(S)}\)
\(=\dfrac{1}{6}\)
(iv) Let \(E = \{1, 2, 3, 4, 5\}\)D be the event of the occurrence of a number greater than 6. Accordingly, \(D = Φ\)
\(∴P(D)=\dfrac{\text{Number } \text{of }\text{ outcomes }\text{ favorable} \text{ to }D}{\text{Total } \text{number }\text{ of}\text{ possible }\text{outcomes }}\)
\(=\dfrac{n(D)}{n(S)}\)
\(=\dfrac{0}{6}\)
\(=0\)
(v) Let \(E\) be the event of the occurrence of a number less than 6. Accordingly, \(E = \{1, 2, 3, 4, 5\}\)
\(∴P(E)=\dfrac{\text{Number } \text{of }\text{ outcomes }\text{ favorable} \text{ to }E}{\text{Total } \text{number }\text{ of}\text{ possible }\text{outcomes }}\)
\(=\dfrac{n(E)}{n(S)}\)
\(=\dfrac{5}{6}\)
Top Questions on Axiomatic Approach to Probability
- In Class XI of a school 40% of the student's study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
- CBSE Class XI
- Mathematics
- Axiomatic Approach to Probability
- In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i)The student opted for NCC or NSS.
(ii)The student has opted neither NCC nor NSS.
(iii)The student has opted NSS but not NCC- CBSE Class XI
- Mathematics
- Axiomatic Approach to Probability
- A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine
- P(not A)
- P (not B)
- P(A or B)
- CBSE Class XI
- Mathematics
- Axiomatic Approach to Probability
Three coins are tossed once. Find the probability of getting
(i) 3 heads (ii) 2 heads (iii) at least 2 heads
(iv) at most 2 heads (v) no head (vi) 3 tails
(vii) exactly two tails (viii) no tail (ix) at most two tails- CBSE Class XI
- Mathematics
- Axiomatic Approach to Probability
- Check whether the following probabilities P(A) and P(B) are consistently defined
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8- CBSE Class XI
- Mathematics
- Axiomatic Approach to Probability
Questions Asked in CBSE Class XI exam
- Draw formulas for the first five members of each homologous series beginning with the following compounds.\((a) H–COOH (b) CH_3COCH_3 (c) H–CH=CH_2\)
- CBSE Class XI
- Organic Chemistry- Some Basic Principles and Techniques
- Distinguish between the following pairs of sentences.
(i) He was visibly moved.
(ii) He was visually impaired.- CBSE Class XI
- The adventure
- How, according to you, can peace and liberty be maintained in a state?
- CBSE Class XI
- The tale of melon City
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- CBSE Class XI
- Pressure
- Describe the change in hybridisation (if any) of the Al atom in the following reaction.
\(AlCl_3+Cl^- \rightarrow AlCl_4^-\)- CBSE Class XI
- Hybridisation
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.