Determine the probabilities We roll a die 10 times. What is the probability that

Question

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

Explanation / Answer

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

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