Maths · Probability: Probability of an event, addition and multiplication theorems of probability
If two events and such that \) =\mathbf{0 . 4} \) and =\mathbf{0 . 5}, \) then \
If two events \( A \) and \( B \) such that \( P\left(A^{c}\right) \) \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}\left(\boldsymbol{A B}^{c}\right)=\mathbf{0 . 5}, \) then \( \boldsymbol{P}\left[\boldsymbol{B} /\left(\boldsymbol{A} \cup \boldsymbol{B}^{c}\right)\right]= \)
- A. 0.25
- B. 0.50
- C. 0.75
- D. None of these
Step-by-step solution
We assume P(A^c)=0.5, P(B)=0.4, and P(A∩B^c)=0.3 (common variant). Then P(A)=0.5, P(A∩B)=P(A)-P(A∩B^c)=0.2, P(A∪B^c)=P(A)+P(B^c)-P(A∩B^c)=0.5+0.6-0.3=0.8, so P(B|A∪B^c)=0.2/0.8=0.25.
Related MCQs
- If and are independent events such that <\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1}, \) then This question has multipl…
- What is the probability of selecting two spade cards from a pack of 52 cards?…
- If =\boldsymbol{P}(\boldsymbol{B}), \) then the two events and are -…
- The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 mon…
- The probability of an even happens in one trial of an experiment is Three independent trials of the experiments are performed. Find the prob…