A box contains 12 mangoes out of which 4 are spoilt.
If four mangoes are chosen at random, find the
probability that
1. all the four mangoes are spoilt.
494
394
(A) 495
(B) 495
(C) 395
(D) 395
2. atleast one mango is good.
494
(A) 495
(B) 395
(0) 495
(D) 305
3.exactly three are good mangoes.
224
129
(A)
495
495
495
116
Answers
Step-by-step explanation:
p(m1)=number of favorite outcomes of mango of m1÷ total number of possible outcomes of language =4÷4=1
p(m2)=at least one mango is good =1÷4=1/4
p(m3)=exactly three are good mangoes=3÷4=3/4
HOPE. IT. HELPS. U
The probability that
1. all four mangoes are spoilt = [1/495] or 2.02 * 10⁻³
2. at least one mango is good = [494/495] or 0.99
3.exactly three are good mangoes = [224/495] or 0.45
Step-by-step explanation:
Required Formula:
nCr = [n!] / [(n-r)!*r!]
Total no. of mangoes in the box = 12
No. of rotten mangoes = 4
The probability of choosing 4 mangoes at random for each of the given cases are as follows:
Case 1: All four mangoes are spoilt
Total no. of outcomes
= ¹²C₄ = [12!] / [(12-4)! * 4!]
= [12*11*10*9*8!]/[8!*4*3*2]
= 495
And,
No. of favourable outcomes = 4C4 = [4!] / [(4-4)! * 4!] = 1
∴ The probability of getting all four mangoes being spoilt is,
= [No. of favourable outcomes] / [Total no. of outcomes]
= [1/495] or 2.02 * 10⁻³
Case 2: At least one mango is good
Here, to get at least one mango good we will subtract the case of all mangoes being spoilt from 1.
∴ The probability of getting at least one mango good is,
= 1 - [{No. of favourable outcomes of all 4 mangoes being spoilt} / {Total no. of outcomes}]
= 1 – [1/495]
= [494/495] or 0.99
Case 3: Exactly three are good mangoes
No. of good mangoes = 12 – 4 = 8
So,
No. of favourable outcomes
= (3 good mangoes) * (1 spolit mango)
= ⁸C₃ * ⁴C₁
= [8!/(5!*3!)] * [4!/(3!*1!)]
= 56 * 4
= 224
∴ The probability of getting exactly three good mangoes is,
= [No. of favourable outcomes] / [Total no. of outcomes]
= [224/495] or 0.45
-------------------------------------------------------------------------------------------
Also View:
Find the Probability of Getting One Rotten Egg In a container there are 28 eggs out of which 8 eggs are rotten, if 2 eggs are chosen at random, what will be the probability that at least one egg is rotten?
https://brainly.in/question/637897
The probability of a defective egg in a lot of 400 eggs is 0.035.calculate the number of defective eggs in the lot.also calculate the probability of taking out an non defective egg from the lot.
https://brainly.in/question/2776472
There are 4 rotten eggs in a lot containing 20 eggs. Find the probability of getting a rotten egg if 2 eggs are chosen at random ?
https://brainly.in/question/14235549