Q.4.25 - A First Course in Probability

Question

 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].

Step-by-Step Solution

Answer

1. $P\{x=1\}=0.46$
2. $E\left[x\right]=1.3$
   

Step 1: 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 $P(x=1)$

Step 2: Explanation (Part a)

Here,  $P(x=1)$

So,

$P\{x=1\}=P (First coin heads and second coin tails + First coin tails and second coin heads)$

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

$=0.46$

Step 3: Final Answer (Part a)

The $P(x=1)$ is $0.46$

Step 4: 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 $E\left(x\right)$

Step 5: Explanation (part b)

$P(x=0)=P (First coin tail \times Second coin tail)$

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

$=(.4\times .3)$

$=0.12$

Here, 

$P(x=2)=P (First coin head \times Second coin head)$

$=(0.6\times 0.7)$

$=0.42$

Therefore, 

$E\left(X\right)=\sum xP\left(x\right)$

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

$=1.3$

Step 6: Final Answer (Part b)

The determined value of $E\left(x\right)$is $1.3$