Mathematics, 05.08.2020 02:01 maualca

Based on a poll, 40% of adults believe in reincarnation. Assume that 4 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. Required:a. The probability that exactly 3 of the 4 adults believe in reincarnation is? b. The probability that all of the selected adults believe in reincarnation is? c. The probability that at least 3 of the selected adults believe in reincarnation is? d. If 4 adults are randomlyselected, is 3 a significantly high number who believe inreincarnation?

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Answer from: Jmarie08

Complete Question

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P(3) = 0.154

P(4) = 0.026

$P( X \ge 3 ) = 0.18$

option C is correct

Step-by-step explanation:

From the question we are told that

The probability of success is p = 0.4

The sample size is n= 4

This adults believe follow a binomial distribution is because there are only two outcome one is an adult believes in reincarnation and the second an adult does not believe in reincarnation

The probability of failure is mathematically evaluated as

q = 1 - p

substituting values

q = 1 - 0.4

q = 0.6

Considering a

The probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as

$P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}$

substituting values

$P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}$

Here $\left 4} \atop {}} \right.C_3$ means 4 combination 3 . i have calculated this using a calculator and the value is

$\left 4} \atop {}} \right.C_3 = 4$

P(3) = 4* (0.4)^3 * (0.6)

P(3) = 0.154

Considering b

The probability that all of the selected adults believe in reincarnation is mathematically represented as

$P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}$

substituting values

$P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}$

Here $\left 4} \atop {}} \right.C_3$ means 4 combination . i have calculated this using a calculator and the value is $\left 4} \atop {}} \right.C_4 = 1$

P(4) = 1* (0.4)^4 * 1

=> P(4) = 0.026

Considering c

the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as

$P( X \ge 3 ) = P(3 ) + P(n )$

substituting values

$P( X \ge 3 ) = 0.154 + 0.026$

$P( X \ge 3 ) = 0.18$

From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is p(4) = 0.026 < 0.05

But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is $P(3) = 0.154 \ which \ is \ 0.05$

Hence 3 is not a significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.