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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

If a die is rolled 4 times, what is the probability that a number greater than 4 is rolled at least 2 times?

To determine

To calculate: The probability of getting a number greater than 4 at least 2 times when a dice is rolled.

Explanation

Given Information:

A dice is rolled 4 times. Then the probability of getting a number greater than 4 at least 2 times

when a dice is rolled.

Formula used:

For a binomial distribution the probability is,

Pr(x)=(Cxn)pxqnx

Where n the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

q=1p

And,

Cxn=nxnx

Calculation:

Consider A dice is rolled 4 times.

The sample spaces f a die when it is rolled is total 6 as {1,2,3,4,5,6}. Then the numbers greater than 4 are {5,6}.

So, the probability of getting a number greater than 4 is,

p=26=13

Then the probability of failure i.e. of getting number lesser than 4,

q=1p=113=23

So, the probability of getting a number greater than 4 at least 2 time is,

1Pr(0)Pr(1)=1(C0n)pxqnx(C1n)pxqnx

Where n=4,x=0,p=13,q=23 and n=4,x=1,p=13,q=23

Now,

1Pr(0)Pr(1)=1(C0n)pxqnx(C1n)pxqnx=1(C04)(13)0(23)

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