Question

3. Calculate the following probabilities: a. Getting at least one 1 in four rolls of a single die. b. Getting rain at least once in ten days if the probability of rain on each single day is 0.1.

Answer 1

3 a. Probability of getting atleast one 1 in 4 four rolls
Using binomial probability distribution
Number of trial(n) =4
Probability (p) of getting 1 =1/6
q =1-1/6 =5/6

Probability of getting atleast one 1 =1-Probability of getting no 1s =1-P(X=0) =1-ⁿC_xp^xq^(n-x) =1-4C0*(1/6)^0*(5/6)^4 =1-(5/6)^4 =
0.5177 or 0.52

b. n =10
p=0.1
q =1-0.1 =0.9
Probability of getting rain in atleast on day =1 -Probability of no rain in any day =1-ⁿC_xp^xq^(n-x) =1-10C0*(0.1)^0*(0.9)^10
=1-(0.9)^10 =0.6513 or 0.65