   Chapter 14.CT, Problem 14CT ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# An unbalanced coin weighted so that the probability of heads is 0.55 . The coin is tossed ten times.(a) What is the probability of getting exactly 6 heads?(b) What is the probability of getting fewer than 3 heads?

To determine

(a)

To find:

The probability of getting exactly 6 heads.

Explanation

Given:

The probability of getting head in a biased coin is 0.55 and the coin is tossed ten times.

Approach:

The formula of probability of an event is given by,

P(rsuccessesinntrials)=C(n,r)prqnr

Here, r is the number of success required in n number of trails, p is the probability of success and q is the probability of failure.

The formula for C(n,r) is given by,

C(n,r)=n!r!(nr)!

Calculation:

The probability of getting head in a biased coin is 0.55 so,

p=0.55

Sum of total probability is equal to 1 so the probability of failure is,

q=10.55=0.45

Substitute 0.55 for p, 0.45 for q, 6 for r and 10 for n in above equation.

To determine

(b)

To find:

The probability of getting fewer than 3 heads.

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