Question

In four throws with a pair of dice, the probability of throwing a double at least once is

• A. ${\left(\frac{5}{6}\right)}^4$
• B. $1-{\left(\frac{5}{6}\right)}^4$
• C. ${\left(\frac{5}{6}\right)}^4{+}_1^{4}C{\left(\frac{5}{6}\right)}^3{\left(\frac{1}{6}\right)}^1$
• D. ${}_1^{4}C{\left(\frac{5}{6}\right)}^3{\left(\frac{1}{6}\right)}^1$

Answer 1

The correct option is B $1-{\left(\frac{5}{6}\right)}^4$

Probability of throwing a double at least once is $=$ 1 $-$ Probability of none are doubles
$6$ cases when all are doubles: $11,22,33,44,55,66$
Probability of none are doubles $=(1-(\frac{1}{6}{)}^4)=(\frac{5}{6}{)}^4$
Probability of throwing a double at least once is $=1-(\frac{5}{6}{)}^4$