The probability of finding a green signal on a busy crossing X is 30 % . What is the probability of finding a green signal on X on two consecutive days out of three?

Let A be the event of finding a green signal on a busy crossing X The probability of finding a green signal on a busy crossing X is 30 % . P A = 30 100 = 3 10 The probability of not finding a green signal on a busy crossing X is P A ¯ = 1 - 3 10 = 7 10 . The probability of finding a green signal on X on two consecutive days out of three = P A P A P A ¯ + P A ¯ P A P A = 3 10 × 3 10 × 7 10 + 7 10 × 3 10 × 3 10 = 63 500 .

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When a new partner is admitted into the partnership, which account is credited for the decrease in the value of liabilities?

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Important Questions on Ray Optics and Optical Instruments

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Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

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A

and

B

are two events such that

P (A) \neq 0

and

P (B| A) = 1

, then

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Let

A

and

B

be two non-null events such that

A \subset B .

Then, which of the following statements is always correct?

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A and B

are two independent events with

P (A) = \frac{1}{3} and P (B) = \frac{1}{4}

, then

P (B^{'} ∣ A)

is equal to

EASY

Physics>Optics>Ray Optics and Optical Instruments>Optical Instruments

The probability of finding a green signal on a busy crossing

X

30 %

. What is the probability of finding a green signal on

X

on two consecutive days out of three?

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A black and a red die are rolled together. Find the conditional probability of obtaining the sum

8

, given that the red die resulted in a number less than

4

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Let

n_{1} & n_{2}

be the number of red and black balls, respectively, in box

I

. Let

n_{3} & n_{4}

be the number of red and black balls, respectively, in box

II

. A ball is drawn at random from box

I

and transferred to box

II

. If the probability of drawing a red ball from box

I

, after this transfer, is

\frac{1}{3}

, then the correct options(s) with the possible values of

n_{1} & n_{2}

is(are)

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Ten cards numbered

1

10

are placed in box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than

3

, what is the probability that it is an even number ?

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In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

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An urn contains

5

red and

2

green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

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A and B are two events such that P(A)

\neq

0. Find P(B/A) if A

\subset

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Four persons can hit a target correctly with probabilities

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

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A family has two children. What is the probability that both children are boys, given that at least one of them is a boy?

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It is given that events

A

and

B

are such that

P (A) = \frac{1}{4}, P (A ∣ B) = \frac{1}{2}

and

P (B ∣ A) = \frac{2}{3}

, then

P (B)

is equal to

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An unbaised die is thrown twice. Let the event A be "odd number on the first throw" and B the event "odd number on the second throw". Check the independence of the events A and B.

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A manufacturer has three machine operators

A, B

and

C

. The first operator

A

produces

1 %

of defective items, whereas the other two operators

B

and

C

produces

5 %

and

7 %

defective items respectively.

A

is on the job for

50 %

of the time.

B

on the job

30 %

of the time and

C

on job for

20 %

of the time. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by

A ?

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A bag contains

4

red and

6

black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

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A

and

B

are any two events such that

P (A) + P (B) - P (A a n d B) = P (A)

, then

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A die marked

1, 2, 3

in red

4, 5, 6

in green tossed. Let

A

be the event "number is even" and

B

be the event "number is marked red". Find whether the events

A

and

B

are independent or not.

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A problem in mathematics is given to three students

A, B, C

and their respective probability of solving the problem is

\frac{1}{2}, \frac{1}{3}

and

\frac{1}{4}

, the probability that the problem will be solved is

When a new partner is admitted into the partnership, which account is credited for the decrease in the value of liabilities?

Important Questions on Ray Optics and Optical Instruments

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