Determine the probabilities We roll a die 10 times What is t

Determine the probabilities

We roll a die 10 times. What is the probability that we get the outcome of “1” three times from the ten trials?

A group of people are offered possible wonderful vacation packages to Hawaii. It gives three tickets to us: one for a man and two for women. There are 5 men and 10 women in my group. When we select one man and two women, what is the probability that both I and my fiancé (all are in the group) are selected?

The weight of students in an engineering college follows a normal distribution, N(125, 20) (lb). When we select a student, find the probability that the selected student has the weights less than 118 lb.

The weight of students in an engineering college follows a normal distribution, N(125, 20) (lb). When we select five students, find the probability that the calculated sample mean of the weight is less than 118 lb

Solution

this is binomial distribution n=10, p=1/6

we need P(x=3)

use =BINOM.DIST(3,10,1/6,) in excel we get 0.1551

Possible ways=5C1*10C1

total outcomes=15C2

Prob=5C1*10C1/15C2=50/105=0.47619

use NORM.DIST(118,125,20,TRUE) in excel, we get, 0.3632

for sample mean

E(sample mean)=125

sd(sample mean)=20/sqrt(5)=8.9442

using NORM.DIST(118,125,8.9442,TRUE) in excel we get 0.2169