For each of the following situations, state the probabilty rule or rules that yo

Question

For each of the following situations, state the probabilty rule or rules that you would use and apply it or them. Write a sentence explaining how the situation illustrates the use of the probablity rules.

a. The probability of event A is 0.417. What is the probability event A does NOT occur?

b. A coin is tossed 4 times. The probability of zero heads is 1/16 and the probability of zero tails is 1/16. What's the probability that all four tosses result in the same outcomes?

c. Refer to part b. What's the probability that there is at least one head and at least one tail.

d. The probabilty of event A is 0.4 and the probability of event B is 0.8. Events A and B are disjoint. Can this happen?

e. Event A is very rare. Its probability is -0.04. Can this happen?

Explanation / Answer

a) P(A)=0.417

P(A')=1-P(A)

=1-.417=0.583

b)A coin is tossed 4 times. The probability of zero heads is 1/16 and the probability of zero tails is 1/16. What's the probabilit

P(H=0)=1/16 ,P(T=0)1/16

P(AUB)=P(A)+P(B) using addition rule

P(AnB)=

p(AUB)=1/16+1/16=2/16

c)P(AUB)=1-P(at least one head and one tail)

P(atleast one head and at least one tail)=1-P(AUB)

=1-2/16=14/16

d)P(A)=0.4 ,P(B)=0.8

if Ad B are disjoint mans there is no common outcomes

i.e. P(AUB)=P(A)+P(B)=0.4+0.8=1.2 ,(P(AnB)=0)

Probability never more than 1

this is not happen.

e )Prob is always lies between 0 to 1

i.e. prob never negative

defication of prob if A is the event that

0<=P(A)<=1

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