Problem Solving

Please explain,

A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
A) 1/5
B) 3/10
C) 2/5
D) 1/2
E) 3/5

My first thoughts: There are 10 possible ways to choose 2 apples from 5.
But the answer seems to indicate it is much more straight forward than that.
Answer below:





C) 2/5

Probability = Favorable/Total

There are 10 possible ways to choose 2 apples from 5.
Favorable = 1 spoiled apple and 1 good apple
Ways of selecting the spoiled apple = 1
Ways of selecting the good apple = 4C1
so favorable = 1*4

Probability = 4/10 or 2/5

There is 1 rotten apple out of 5 so the probability that of picking an that rotten apple is 1/5
now you have to pick it 2 times.

each time when you pick it up the probability that it it will be a rotten apple is 1/2.

so the resultant will be a product of all these probabilities: 1/2*1/5*2= 1/5

Any corrections

Thanks
Komal Joshi
===============
www.testinggeek.com

Hi Komal,

The questions asks "A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?"

So the event here is picking up two apples from the baskets, so that 1 will be spoiled & the other will be a good one.

The way u have solved it is for an event wherein we need to pick two apples one by one with replacement so that both the times we pick a spoiled apple & BTW in that case also the reqd probabilty will be 1/5*1/5

Hope this helps.