Chapter 7: Q. 2.5 (page 438)

Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?
$a . 4 (16) 3 (56) 14 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} b . (16) 3 (56) 1 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} c . 4 (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} d . (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} e . 6 (16) 1 (56) 3^{6} {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

Short Answer

Expert verified

The probability that a 6 occurs on exactly one of the rolls is $4 (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$ .

Step by step solution

Given Information

Let roll four times with a fair die

Formula used:

$P (X = r) = {}^{n}C_{1} (p)^{r} (q)^{n - r}$

Explanation for correct option

Because each die roll is unique,

$X ~ binomial (4, 1 / 6)$

$P (X = 1) = {}^{4}C_{1} {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

$= 4 \times \frac{1}{6} \times {(\frac{5}{6})}^{3}$

Therefore, the correct option is (c)

Explanation for incorrect option

(a) The probability that a 6 occurs on exactly one of the rolls is not $4 (16) 3 (56) 14 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1}$

(b) The probability that a 6 occurs on exactly one of the rolls is not $(16) 3 (56) 1 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1}$

(d) The probability that a 6 occurs on exactly one of the rolls is not $(16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

(e) The probability that a 6 occurs on exactly one of the rolls is not $6 (16) 1 (56) 3^{6} {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

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Car Number	Color	Age
$1$	Red	$1$
$2$	White	$5$
$3$	Silver	$8$
$4$	Red	$20$

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Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?a.4(16)3(56)14163561b.(16)3(56)1163561c.4(16)1(56)3161563d.(16)1(56)3161563e.6(16)1(56)36161563

Short Answer

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Given Information

Explanation for correct option

Explanation for incorrect option

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