Question

I flip a fair coin and recorded the result. If it is head, I then roll a 6-sided die: otherwise, I roll a 4-sided die and record the results. Let event A be the die has a 3 or greater. let event B be I flip tails. (a)-List all the outcomes in the Sample space (b)- List the outcomes in Event A and B (c)- List the outcomes in A or not B (d)- Calculate the probability of event A (e) Calculate the probability of A and not B.

Answer 1

Solution:-

Given data:-

Consider event A be the die has a 3 or greater.

Consider event B be I flip tails.

(a)List all the outcomes in the Sample space

The sample space has the following outcomes for this experiment:

First outcome (H,1)

Second outcome (H,2)

Third outcome (H,3)

Fourth outcome (H,4)

Fifth outcome (H,5)

Sixth outcome (H,6)

Seventh outcome (T,1)

Eighth outcome (T,2)

Ninth outcome (T,3)

Tenth outcome (T,4)

So there are total 10 outcomes.

(b) List the outcomes in Event A and B

The outcomes in Event A and B are { (T,3), (T,4) }

(c) List the outcomes in A or not B

For event A, the outcomes are { (H,3), (H,4), (H,5), (H,6), (T,3), (T,4) }

For event B, the outcomes are { (H,1), (H,2), (H,3), (H,4), (H,5), (H,6) }

For event A not event B, the outcomes are { (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,3), (T,4) }

(d) Calculate the probability of event A

Number of outcomes in A = 6

Total outcomes = 10

Probability of event A = 6/10 = 0.6

The probability of event A = 0.6

(e) Calculate the probability of A and not B.

For event A and not event B,the outcomes are { (H,3), (H,4), (H,5), (H,6) }

Total outcomes = 10

The probability of A and not B = 4/10 =0.4

The probability of A and not B = 0.4