Chapter 4: Q.4.25 (page 165)

Two coins are to be ﬂipped. The ﬁrst coin will land on heads with probability . $6$ , the second with probability . $7$ . Assume that the results of the ﬂips are independent, and let X equal the total number of heads that result. (a) Find P{X = $1$ }. (b) Determine E[X].

Short Answer

Expert verified

$P {x = 1} = 0.46$
$E [x] = 1.3$

Step by step solution

Given information (part a)

Given in the question that, two coins are to be flipped.

The ﬁrst coin will land on heads with probability 6.

The second with probability 7.

We need to find $P (x = 1)$

Explanation (Part a)

Here, $P (x = 1)$

So,

localid="1647060561473" $P {x = 1} = P (F i r s t c o i n h e a d s a n d s e c o n d c o i n t a i l s + F i r s t c o i n t a i l s a n d s e c o n d c o i n h e a d s)$

$= 0.6 \times 0.3 + 0.4 \times 0.7$

localid="1647060568419"

= 0.46

Final Answer (Part a)

The $P (x = 1)$ is $0.46$

Given information (Part b)

Given in the question that, two coins are to be flipped.

The ﬁrst coin will land on heads with probability 6.

The second with probability 7.

We need to determine $E (x)$

Explanation (part b)

$P (x = 0) = P (F i r s t c o i n t a i l \times S e c o n d c o i n t a i l)$

$= (1 - 0.6 \times 1 - 0.7)$

localid="1647061685180" $= (. 4 \times . 3)$

$= 0.12$

Here,

$P (x = 2) = P (F i r s t c o i n h e a d \times S e c o n d c o i n h e a d)$

$= (0.6 \times 0.7)$

$= 0.42$

Therefore,

$E (X) = \sum x P (x)$

$= 0 \times 0.12 + 1 \times 0.46 + 2 \times 0.42$

$= 1.3$

Final Answer (Part b)

The determined value of $E (x)$ is $1.3$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Two coins are to be ﬂipped. The ﬁrst coin will land on heads with probability . $6$ , the second with probability . $7$ . Assume that the results of the ﬂips are independent, and let X equal the total number of heads that result. (a) Find P{X = $1$ }. (b) Determine E[X].

Short Answer

Step by step solution

Given information (part a)

Explanation (Part a)

Final Answer (Part a)

Given information (Part b)

Explanation (part b)

Final Answer (Part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Two coins are to be ﬂipped. The ﬁrst coin will land on heads with probability .6, the second with probability .7. Assume that the results of the ﬂips are independent, and let X equal the total number of heads that result. (a) Find P{X =1}. (b) Determine E[X].

Short Answer

Step by step solution

Given information (part a)

Explanation (Part a)

Final Answer (Part a)

Given information (Part b)

Explanation (part b)

Final Answer (Part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Two coins are to be ﬂipped. The ﬁrst coin will land on heads with probability . $6$ , the second with probability . $7$ . Assume that the results of the ﬂips are independent, and let X equal the total number of heads that result. (a) Find P{X = $1$ }. (b) Determine E[X].