In a study conducted by the Bank of America, it was found that 34% of young Millenials say that they sleep with their smartphone on their bed. If four Millenials are selected at random what is the probability that:
a) None of them sleep with their phone on their bed?
b) Exactly two sleep with their phone on their bed?
c) At least two of them sleep with their phone on the bed?
What I know: n=4, p=34/100 q= 66/100 from 1-34/100
for a I got .1897
p(x=0) c(4,0) (34.100)^0 (66/100)^4
and for part b I got .3021
p(x=2) c(4,2) (34/100)^2 (66/100)^2
but I'm stuck on part c.
p yes = .34
q no=1-p = 1-.34 = .66
a. yes n = 4,
none of them C(4,0) .34^0 * .66^4 = 1 * 1 * .66^4 = .1897 yes
b. C(4,2) .34^2 .66^2 = 6 * .1156* .4356 = .3021 yes
c. prob( 2 or 3 or 4) = 1 - (just one + none )
prob of zero = .1897 we know from part a
prob of one = C(4,1).34^1 * .66^3 = 4 * .34* .2875 = .3910
sum = .5807
1 - .5807 = .4193
You sure have raced through this subject in two days !
To calculate the probability that at least two out of four Millennials sleep with their phone on their bed, you can calculate the probability of each scenario where two, three, or all four of them sleep with their phone on their bed, and then add up those probabilities.
Let's break it down:
1. Probability of exactly two sleeping with their phone on their bed:
You already calculated this correctly in part b. The probability of exactly two Millennials sleeping with their phone on their bed is 0.3021.
2. Probability of exactly three sleeping with their phone on their bed:
To calculate this probability, you can use the binomial probability formula. The probability of exactly three Millennials sleeping with their phone on their bed can be calculated as:
p(x = 3) = C(4, 3) * (34/100)^3 * (66/100)^1
Here, C(4, 3) represents the number of ways to choose 3 out of 4 Millennials. Plug in the values and calculate the probability.
3. Probability of all four sleeping with their phone on their bed:
Similarly, the probability of all four Millennials sleeping with their phone on their bed can be calculated as:
p(x = 4) = C(4, 4) * (34/100)^4 * (66/100)^0
Again, C(4, 4) represents the number of ways to choose 4 out of 4 Millennials. Calculate the probability.
4. Add up the probabilities:
To find the probability of at least two Millennials sleeping with their phone on their bed, you need to add up the probabilities of exactly two, three, and four sleeping with their phone on their bed:
p(at least two) = p(x = 2) + p(x = 3) + p(x = 4)
Calculate this sum to get the final probability.
Note: Make sure to use the correct values for n (number of trials), p (probability of success), and q (probability of failure or complement of p) in all the calculations.