Probability, Course Quiz (Inter 2nd Year)

The conditional probability

P(E \mid F)

, for

P(F) \ne 0

, is defined as

A

\displaystyle \dfrac{P(E \cap F)}{P(E)}

B

\displaystyle \dfrac{P(E)}{P(F)}

C

P(E)P(F)

D

\displaystyle \dfrac{P(E \cap F)}{P(F)}

A

and

B

are independent with

P(A) = 0.4

and

P(B) = 0.25

. Find

P(A \cap B)

.

A

0.55

B

0.65

C

0.1

D

0.15

If

A

and

B

are mutually exclusive with

P(A) > 0

and

P(B) > 0

, then

A

and

B

are

A complementary

B always independent

C not independent

D independent only if

P(A) = P(B)

Two dice are thrown. Given that the first shows

3

, find the probability that the sum is

8

.

A

\displaystyle \tfrac{1}{6}

B

\displaystyle \tfrac{1}{36}

C

\displaystyle \tfrac{1}{3}

D

\displaystyle \tfrac{5}{36}

A box has

3

red and

2

blue balls. Two are drawn without replacement. Find

P(\text{red then blue})

.

A

\displaystyle \tfrac{3}{5}

B

\displaystyle \tfrac{1}{5}

C

\displaystyle \tfrac{6}{25}

D

\displaystyle \tfrac{3}{10}

E

and

F

are independent with

P(E) = 0.3

and

P(F) = 0.6

. Find

P(E' \cap F')

.

A

0.18

B

0.28

C

0.1

D

0.72

Two students solve a problem independently with probabilities

\displaystyle \tfrac{1}{2}

and

\displaystyle \tfrac{2}{3}

. Find the probability that the problem is solved.

A

\displaystyle \tfrac{7}{6}

B

\displaystyle \tfrac{1}{3}

C

\displaystyle \tfrac{1}{2}

D

\displaystyle \tfrac{5}{6}

Machines A and B make

70\%

and

30\%

of a factory's items, with defect rates

3\%

and

5\%

. Find the probability that a random item is defective.

A

0.021

B

0.08

C

0.036

D

0.04

In the previous situation (shares

70\%

,

30\%

; defect rates

3\%

,

5\%

), an item is defective. Find the probability that machine B made it.

A

\displaystyle \tfrac{5}{8}

B

0.3

C

\displaystyle \tfrac{5}{12}

D

\displaystyle \tfrac{7}{12}

A condition affects

2\%

of people. A test detects it in

90\%

of those who have it and gives a false positive for

10\%

of those who do not. Find

P(\text{condition} \mid \text{positive})

.

A

\displaystyle \tfrac{9}{58}

B

0.018

C

\displaystyle \tfrac{9}{49}

D

0.9

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