3 rotten apples are mixed with 7 good apples in a box. Three apples are chosen simultaneously from the box.Find the probability distribution of 'number of good apples'. Also, find its mean and variance.
Answers
Mean = 2.1 & Variance = 0.63 if Three apples are chosen simultaneously from the box with 3 rotten apples mixed with 7 good apples
Step-by-step explanation:
3 rotten apples are mixed with 7 good apples in a box.
=> Probability of rotten apple = 3/10 =0.3
Probability of good apple = 7/10 = 0.7
Three apples are chosen
0 good apples = ³C₀ (0.7)⁰(0.3)³ = 0.3³ = 0.027
1 good apple = ³C₁ (0.7)¹(0.3)² = 2.1 * 0.3² = 0.189
2 good apples = ³C₂ (0.7)²(0.3)¹ = 0.7² * 0.9 = 0.441
3 good apple = ³C₃ (0.7)³(0.3)⁰ = 0.7³ = 0.343
P(0) = 0.027
p(1) = 0.189
p(2) = 0.441
p(3) = 0.343
Mean = 0*0.027 + 1 * 0.189 + 2 *0.441 + 3 *0.343
= 0 + 0.189 + 0.882 + 1.029
= 2.1
Mean of Good Apples = 2.1
Direct method Mean = np = 3 * 0.7 = 2.1
Variance = npq = 3 * 0.7 * 0.3 = 0.63
Learn More:
If the probability of selecting a defective bolt is 0.1, find (1) the mean ...
https://brainly.in/question/11773467
The probability distribution of a random variable X is as - Brainly.in
https://brainly.in/question/5597791
3 rotten apples are mixed with 7 good apples in a box
https://brainly.in/question/13406597
https://brainly.in/question/13424561