MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Engineering Mathematics

Independent and Dependent Events

E1 and E2 are...

Question

$E_{1} a n d E_{2}$ are events in a probability space satisfying the following constraints $P (E_{1}) = P (E_{2}); P (E_{1} \cup E_{2}) = 1; E_{1} a n d E_{2}$ are independent then $P (E_{1}) =$

A

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{1}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 1
$L e t P (E_{1}) = P (E_{2}) = p$ then using Addition theorem of probability

$P (E_{1} \cup E_{2}) = P (E_{1}) + P (E_{2}) - P (E_{1} \cap E_{2})$

$[∵ i n c a s e o f i n d e p e n d e n t e v e n t s P (E_{1} \cap E_{2}) = P (E_{1}) P (E_{2})]$

$1 = p + p - p^{2}$
$o r p^{2} - 2 p + 1 = 0$
$o r p = 1$

Suggest Corrections

thumbs-up

1

Similar questions

E_{1}

E_{2}

are two events such that

P (E_{1}) = \frac{1}{4}, P (\frac{E_{2}}{E_{1}}) = \frac{1}{2}

P (\frac{E_{1}}{E_{2}}) = \frac{1}{4},

then which of the following is/are correct?

E_{1}

E_{2}

are two events such that

P (E_{1}) = \frac{1}{4}

P (\frac{E_{2}}{E_{1}}) = \frac{1}{2}

P (\frac{E_{1}}{E_{2}}) = \frac{1}{4}

E_{1}

E_{2}

are two events such that

P (E_{1}) = 1 / 4, P (E_{2} / E_{1}) = 1 / 2

P (E_{1} / E_{2}) = 1 / 4

E_{1}

E_{2}

are two events such that

P (E_{1}) = \frac{1}{4}, P (E_{2}) = \frac{1}{2}; P (\frac{E_{1}}{E_{2}}) = \frac{1}{4},

then choose the correct options.

Q. For any two independent events

E_{1}

E_{2}, P {(E_{1} \cup E_{2}) \cap (_{1}) \cap (_{2})}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Independent and Dependent Events

ENGINEERING MATHEMATICS

Watch in App

explore_more_icon

Explore more

Independent and Dependent Events

Other Engineering Mathematics

Join BYJU'S Learning Program

CrossIcon