Question

1. Two dice are thrown 5 times, what is the probability of that the sum is less than 6 at the most 3 times?

2. 75% of those who try a certain test the fail, if a sample of 20 people is taken. Determine the probability that:

1) Fail at least 7
2) Fail no more than 8
3) Fail between 7 and 11, inclusive both extremes

**please answer both. thanks!!

Answer 1

1)P(sum is less than 6 in one roll of two dice) =10/36

hence P( sum is less than 6 at the most 3 times out of 5 trails)=P(X<=3) =P(X=0)+P(X=1)+P(X=2)+P(X=3)

=⁵C₀(10/36)⁰(26/36)⁵+⁵C₁(10/36)¹(26/36)⁴+⁵C₂(10/36)²(26/36)³+⁵C₃(10/36)³(26/36)²=0.976847

2-1)

P( Fail at least 7)= =0.999970

2)P(Fail no more than 8)=P(X<=8)= =0.000935

3)

P(Fail between 7 and 11, inclusive both extremes)=P(7<=X<=11)==0.040896