Five dice are thrown simultaneously If the occurrence of an even number is considered a success, find the probability - Maths - Probability

Question

Five dice are thrown simultaneously If the occurrence of an even
number is considered a success, find the probability of at most 3
successes

Lovina Kansal · Accepted Answer

Dear student
Let X denote the number of successes in 5 throws of a die and let p be the probability of getting an even number in a single throw of a die
Thenp=36=12 and q=1-p=1-12=12The probability of r successes in five throws of a die is given byP(X=r)=5Cr12r125-r=5Cr125 where r=1,1,2,
,5Therefore, Required probability=P(X≤3)=1-P(X>3)1-P(X=4)+P(X=5)1-5C4124+5C5125=1-532+132=2632=1316
Regards

Five dice are thrown simultaneously. If the occurrence of an even number is considered a success, find the probability of at most 3 successes.