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Toss 4times Suppose you toss a fair coin 4times. Let X=the number of heads you get.

(a) Find the probability distribution ofX.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find P(X3) and interpret the result.

Short Answer

Expert verified

(a)Probability distribution of Xis

(b)

(c)P(X3)=93.75%

Step by step solution

01

Part (a) Step 1: Given information

Given in the question that , you toss a fair coin4times. Let X= the number of heads you get

We need to find the probability distribution ofX.

02

Part (a) Step 2: Explanation

If His heads and Tis tails, there are 16different ways to throw the fair coin four times:

Each of these outcomes has an equal chance of occurring116.

The product of the number of related outcomes and the probability yields the probability distribution of X="the number of heads":

x
0
1
2
3
4
P(X=x)
16
416
616
416
116
03

Part (b) Step 3: Given information 

Given in the question that , you toss a fair coin 4 times. Let X = the number of heads you get

We need to make a histogram of the probability distribution.

04

Explanation(part b)

Consider the given table:

Each bar's width must be equal, and its height must be equal to the probability:

The histogram is around 2 degrees symmetric.

05

Part (c) Step 1: Given information

Given in the question that, you toss a fair coin 4times. Let X= the number of heads you get.

We need to findP(X3).

06

Part (c) Step 2: Explanation

Consider the given table:

Let's add the corresponding probabilities

P(X3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=116+416+616+416=0.9375

We should expect to get 3heard or less in around 93.75or 94of the 100times we perform the quadruple toss of the coin.

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