korporasidn

2021-11-12

1.The probability of Christine getting a new job or going on vacation (or both) is 0.85. If the probability of Christine going on vacation is 0.10 and the probability of Christine getting a new job is 0.75, are the events Christine gets a new job and Christine goes on vacation mutually exclusive?

2. The probability that Isabelle will go trick-or-treating is 0.4. The probability that she will go trick-or-treating or watch a scary movie is 0.65. The probability of Isabelle going trick-or-treating and watching a scary movie is 0.20.

A. What is the probability that Isabelle will not watch a scary movie?

B. What is the probability that Isabelle will watch a scary movie but does not go trick-or-treating?

2. The probability that Isabelle will go trick-or-treating is 0.4. The probability that she will go trick-or-treating or watch a scary movie is 0.65. The probability of Isabelle going trick-or-treating and watching a scary movie is 0.20.

A. What is the probability that Isabelle will not watch a scary movie?

B. What is the probability that Isabelle will watch a scary movie but does not go trick-or-treating?

Nicole Keller

Beginner2021-11-13Added 14 answers

Step 1

1.Given that

The probability of Christine getting a new job$=0.75$

the probability of Christine going on vacation$=0.10$

The probability that getting a new job or going on vacation$=0.85$

Are the events mutually exclusive

2.

The probability that Isabelle will go trick-or-treating$=0.4$

The probability that she will trick or treating and watching a scary movie$=0.20$

The probability that she will trick and treating and watching a scary movie$=0.65$

A. Find The probability that she will not watch a scary movie

B. Find the probability that she will watch a scary movie but not go trick or treating

Step 2

1.

Let A be the event that Christine getting a new job

Let B be the event that Christine going on a vacation

From the given probabilities

$P\left(A\right)=0.75$

$P\left(B\right)=0.10$

$P(A\cup B)=0.85$

Events A and B are mutually exclusive

Because the occurrence of event A will not affect the Occurrence of B

From the formula, if$P(A\cup B)=P\left(A\right)+P\left(B\right)$ A and B can be mutually exclusive events

here$0.75+0.10=0.85$

Step 3

2.

Let A be an event that Isabelle will go on trick or treat

Let B be an event that Isabelle will go on watching a scary movie

From the given probabilities

$P\left(A\right)=0.4$

$P(A\cup B)=0.65$

$P(A\cap B)=0.20$

a) The probability that she will not watch a scary movie

$P\left(\stackrel{\u2015}{B}\right)=1-P\left(B\right)$

P(B) can be calculated from the relation

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$P\left(B\right)=P(A\cup B)-P\left(A\right)+P(A\cap B)$

$=0.65-0.4+0.20$

$=0.45$

$P\left(\stackrel{\u2015}{B}\right)=1-0.45$

$=0.55$

b) The probability that she will watch a scary movie but not go trick or treat

$P(\stackrel{\u2015}{A}\cap B)=P\left(B\right)-P(A\cap B)$

$=0.45-0.20$

$=0.25$

1.Given that

The probability of Christine getting a new job

the probability of Christine going on vacation

The probability that getting a new job or going on vacation

Are the events mutually exclusive

2.

The probability that Isabelle will go trick-or-treating

The probability that she will trick or treating and watching a scary movie

The probability that she will trick and treating and watching a scary movie

A. Find The probability that she will not watch a scary movie

B. Find the probability that she will watch a scary movie but not go trick or treating

Step 2

1.

Let A be the event that Christine getting a new job

Let B be the event that Christine going on a vacation

From the given probabilities

Events A and B are mutually exclusive

Because the occurrence of event A will not affect the Occurrence of B

From the formula, if

here

Step 3

2.

Let A be an event that Isabelle will go on trick or treat

Let B be an event that Isabelle will go on watching a scary movie

From the given probabilities

a) The probability that she will not watch a scary movie

P(B) can be calculated from the relation

b) The probability that she will watch a scary movie but not go trick or treat