Complete question :
70% of a certain species of tomato live after transplanting from pot to garden. Najib transplants 3 of these tomato plants. Assume that the plants live independently of each other. Let X = the number of tomato plants that live.
What is the probability that exactly 2 of the 3 tomato plants live?
You may round your answer to the nearest hundredth.
Answer:
0.44
Step-by-step explanation:
Given that :
P(live after transplanting) = 0.7
Assume plants live independently of each other :
Number of tomatoes transplanted = 3
Number of potatoes that live = x
Probability that exactly 2 of the 3 tomatoes live?
Using binomial probability ;
p = 0.7
1 - p = 1 - 0. 7 = 0.3
P(x = x) = nCx * p^x * (1 - p)^(n-x)
P(x = 2) = 3C2 * 0.7^2 * 0.3^(3-2)
P(x = 2) = 3C2 * 0.7^2 * 0.3^1
P(x = 2) = 3 * 0.49 * 0.3
P(x = 2) = 0.441
= 0.44 ( nearest hundredth)
The probability that exactly 2 of the 3 tomato plants live is 0.44
The given parameters are:
[tex]\mathbf{n =3}[/tex] --- number of transplants
[tex]\mathbf{r = 2}[/tex] -- the number that lives
[tex]\mathbf{p = 70\%}[/tex] --- the probability that a transplant lives
So, the probability that exactly 2 live is calculated using the following binomial probability formula
[tex]\mathbf{P(x = r) = ^nC_r * p^r * (1 - p)^{(n-r)}}[/tex]
This gives
[tex]\mathbf{P(x = 2) = ^3C_2 * 0.7^2 * 0.3^{(3-2)}}[/tex]
[tex]\mathbf{P(x = 2) = ^3C_2 * 0.7^2 * 0.3^1}[/tex]
Evaluate each factor
[tex]\mathbf{P(x = 2) = 3 * 0.49 * 0.3}[/tex]
Multiply
[tex]\mathbf{P(x = 2) = 0.44}[/tex]
Hence, the required probability is 0.44
Read more about probabilities at:
https://brainly.com/question/11234923
