Question

The probability of drawing a heart from a standard deck of cards is 0.25. You record the car do you draw and return the car before shuffling to ensure a binomial distribution. If you do this 20 times, what is the probability that you will draw a heart seven times.

A) 0.888

B) 0.001

C) 0.112

D) 0.473

Answer 1

Answer: C) 0.112

Explanation:

In binomial distribution with parameters n (Total trails) and p (probability of getting success sin each trial) , the probability of getting success in x trials is given by :-

`P(X=x)=^nC_xp^x(1-p)^(n-x)`

Given : The probability of drawing a heart from a standard deck of cards is 0.25

Here , getting heart is the success.

Then p= 0.25

For n= 20

The probability that you will draw a heart seven times i.e. x= 7:

`P(X=7)=^(20)C_7(0.25)^7(1-0.25)^(20-7)`

`P(X=7)=(20!)/(7!(20-7)!)(0.25)^7(1-0.25)^(20-7)\ \ [\because\ ^nC_r=(n!)/(r!(n-r)!)]`

`=(20*19*18*17*16*15*14*13!)/(7!13!)(0.25)^7(0.75)^(13)\\\\=77520(0.00006103515625)(0.0237572640181)\\\\=0.112406195476\approx0.112`

Hence, the probability that you will draw a heart seven times = 0.112

Thus , the correct answer is C) 0.112 .