Question

The probability that Sandra gets a ride to work on any morning is 0.7. The probability that she gets a ride 3 times in a 5-day work week is __, and the probability that she gets a ride at least 2 times in a 5-day workweek is __.

Answer 1

Answer: that is wrong. It isn’t 0.31 and 0.97, because I just got it wrong.

Explanation:

Answer 2

Answer: The probability that she gets a ride 3 times in a 5-day work week is 0.31.

The probability that she gets a ride at least 2 times in a 5-day workweek is 0.97.

Explanation:

By binomial distribution formula:

`P[X=r]=^nC_rp^rq^(n-r)` , where n is the number of trials , r is the number of success, p is the probability of success and q is the probability of failure.

Given : n=5

p = 0.7

q= 1-0.7=0.3

Now, the probability that she gets a ride 3 times in a 5-day work week :

`P[X=3]=^5C_3(0.7)^3(0.3)^(5-3)\\\\=10(0.7)^3(0.3)^2=0.3087\approx0.31`

The probability that she gets a ride at least 2 times in a 5-day workweek :

`P[X\geq2]=1-P[X<2]\\\\=1-(P[X=1]+P[X=0])\\\\=1-(^5C_0(0.7)^0(0.3)^(5)+^5C_1(0.7)^1(0.3)^(5-1))\\\\=1-[(0.3)^5+5(0.7)(0.3)^4]\\\\=1-0.03078=0.96922\approx0.97`