Conditional Probability and Independence, Quiz

P(E) = 0.8

,

P(F) = 0.5

and

P(E \cap F) = 0.3

. Find

P(E \mid F)

.

A

0.4

B

0.375

C

0.6

D

0.15

A die is thrown. Given that the number is even, find the probability that it is greater than

3

.

A

\displaystyle \tfrac{1}{6}

B

\displaystyle \tfrac{2}{3}

C

\displaystyle \tfrac{1}{3}

D

\displaystyle \tfrac{1}{2}

A bag has

4

red and

6

black balls. Two are drawn without replacement. Find the probability that both are red.

A

\displaystyle \tfrac{2}{5}

B

\displaystyle \tfrac{2}{15}

C

\displaystyle \tfrac{4}{25}

D

\displaystyle \tfrac{1}{3}

A

and

B

are independent with

P(A) = 0.5

and

P(B) = 0.2

. Find

P(A \cup B)

.

A

0.6

B

0.7

C

0.5

D

0.1

Two archers hit a target independently with probabilities

\displaystyle \tfrac{1}{2}

and

\displaystyle \tfrac{1}{4}

. Find the probability that the target is hit.

A

\displaystyle \tfrac{3}{8}

B

\displaystyle \tfrac{5}{8}

C

\displaystyle \tfrac{1}{8}

D

\displaystyle \tfrac{3}{4}

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