Bissoy.com
Doctors Medicines MCQs Q&A

The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q, then P (A′) + P (B′) = ?

The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q, then P (A′) + P (B′) = ? Correct Answer <span class="fontstyle0">2 - 2</span><span class="fontstyle2">p </span><span class="fontstyle0">+ </span><span class="fontstyle2">q</span><span class="fontstyle0">.</span>

Concept:

  • P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  • P(A') = 1 - P(A)

 

Calculation:

Given: Probability of simultaneous occurrence of at least one of two events A and B is p

So, P(A ∪ B) = p.

Since probability that exactly one of A, B occurs = q (given), we get:

P(A ∪ B) - P(A ∩ B) = q

⇒ p - P(A ∩ B) = q

⇒ P(A ∩ B) = p - q

As we know, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ p = P(A) + P(B) - (p - q) 

⇒ P(A) + P(B) = p + (p - q) 

⇒ P(A) + P(B) = 2p - q

Now, P (A′) + P (B′) = 1 - P(A) + 1 - P(B)

= 2 -

= 2 - (2p - q)

= 2 - 2p + q.

Related Questions

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.
Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)
Consider the following statements: 1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other. 2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities. Which of the above statements is/are correct?
The probability of occurance of two two events A and B are 1/4 and 1/2 respectively. The probability of their simultaneous occurrance is 7/50. Find the probability that neither A nor B occurs.
Two statements are followed by three Conclusions I, II and III. You have to consider the statements to be true, even if they seem to be at variance from commonly known facts. You are to decide which of the given conclusions can definitely be drawn from the given statements and indicate your answer accordingly. Statements: I. Political parties that opposed simultaneous polls before the Law Commission mostly cited federalism, Constitution and impracticability for their opposition, but Goa Forward Party chose coconuts to drive home its point against the proposal of ‘One Nation, One Election'. II. The regional party that is part of the BJP-led Goa government cited coconut, its party symbol, to argue that regional issues will go unaddressed in the noise of simultaneous polls. Conclusions: I. To buttress its reasoning, Goa Forward Party representative cited the party's history and struggle in protesting against cutting down of coconut trees in Goa before it came to power with ally BJP in March 2017. II. The party had protested against the BJP government's decision to amend rules to simplify the procedure of cutting down coconut trees by removing it from the list of trees. III. The commission held talks with political parties on the proposal of simultaneous elections.
It is estimated that average number of events during an year is three. What is the probability of occurrence of not more than two events over a two year duration? Assume that the number of events follow a Poisson's distribution.
In Lorentzian relativity, if two events are simultaneous for one observer, they will be simultaneous for all other observers as well.
Q.(1-4): Answer the questions on the basis of the information given below. * F,G and H are insurance companies , Q,R,S and T are private detectives .Each detective works for at least one of the insurance companies. * Q always works for F and at least one of the other companies. Some of the time G employs only one of these detectives,' the rest of the time it employs exactly two of them. *F and H each employ exactly two of these detectives all the time. If R works for H only, and if S works for G and H only, T works for--
In a class of 75 students, every student participates in at least one of the three events – music, drama and poetry. 12 students participate in all 3 events. 21 student participate in any two events. If 14 students participate in music only and 15 students participate in drama only, then how many students participate in poetry only? 
Following are the conditions to select a manager for accounts in a company: 1, The candidate must be at least 30 years and not more than 40 years as on 1st January 2019. 2. Be a commerce graduate with at least 55% aggregate marks 3. Have experience of at least 10 years of accounts experience out of which at least 3 years in a managerial position in an organization. 4, Have secured at least 60% in the recruitment process. At 2 above. but has secured at least 50% aggregate marks in graduation and has secured 80% in there cruitment process, he can be referred to VP-accounts. In each question below the candidate details are provided. Read the question and answer based on the information provided. Don’t assume anything. Ram is born on 1 August 1974 and has a 60% aggregate in graduation -he has 15 years" experience in an organization with 5 years as accounts manager.