At a wildlife sanctuary, researchers track the survival of two newly

Question

At a wildlife sanctuary, researchers track the survival of two newly released animal groups. Group A has a 3/5 chance of surviving its first winter, while Group B has a 4/5 chance of surviving its first winter.

Select for  Minimum Survival  the lowest probability, consistent with these estimates, that both groups survive the winter. Select for  Maximum Survival  the highest probability, consistent with these estimates, that both groups survive the winter. Make only two selections, one in each column.

Bunuel · Accepted Answer

• Minimum Survival Probability

We use the equation:

Total = P(A) + P(B) – P(both) + P(neither).

Substitute the values:

1 = 3/5 + 4/5 – P(both) + P(neither).

P(both) = 2/5 + P(neither).

To minimize P(both), we set P(neither) = 0.

This gives P(both) = 2/5.

Alternative we can do the following:

We are given:

P(A) = 3/5 (the probability that Group A survives),
P(B) = 4/5 (the probability that Group B survives).

This means the probability that Group B does not survive is:

P(not B) = 1 - P(B) = 1/5.

Now consider the event “A survives  and  B does not survive.” Its probability cannot be greater than either P(A) = 3/5 or P(not B) = 1/5. Therefore, the  maximum  possible probability of this event, “A survives  and  B does not survive”, is 1/5.

But P(A) = 3/5 represents all cases where A survives, and that breaks into two disjoint parts:

A survives and B survives, and
A survives and B does not survive.

So we can write:

P(A) = P(A and B) + P(A and not B).

We know P(A) = 3/5, and the maximum possible value of P(A and not B) is 1/5.

Therefore, the minimum possible value of P(A and B) is:

P(A and B) = 3/5 - 1/5 = 2/5.

So by this reasoning as well, the minimum survival probability for both is 2/5.

• Maximum Survival Probability

The probability of Group A surviving is 3/5 (60%) and the probability of Group B surviving is 4/5 (80%). The maximum probability that both survive cannot be greater than either one individually. Therefore, the maximum possible value of P(both) is the smaller of the two: 3/5 (60%).

I29-168

findingmyself · Answer

P(A or B)= P(A)+P(B)-P(A and B)+P(Neither) 
 1=0.6+08-P(A and B)+P(Neither)

P(A and B)=P(Neither)+0.4

P(A and B) is minimum when P(Neither) is minimum  
 Min P(A and B)=0.4 or 2/5

Maxmimum of P(A and B)=3/5 which is min of P(A) and P(B)= 3/5

AbhishekP220108 · Answer

Given info 
P(A)=3/5=0.6
P(NOT A)=2/5=0.4

P(B)=4/5=0.8
P(NOT B)=1/5=0.2

Lets form a table to check max and min probability and mark

MAX PROBABILITY 
 P(A) 
 P(NOT A) 
 TOTAL 
 
  P(B) 
 0.60 
 0.2 
 0.8 
 
  P(NOT B) 
 0 
 0.2 
 0.2 
 
  TOTAL 
 0.60 
 0.40 
 1

MIN PROBABILITY 
 P(A) 
 P(NOT A) 
 TOTAL 
 
  P(B) 
 0.40 
 0.4 
 0.8 
 
  P(NOT B) 
 0.2 
 0 
 0.2 
 
  TOTAL 
 0.60 
 0.40 
 1

So max P(A&B)=0.6=3/5
 So min P(A&B)=0.4=2/5

hope it helps

isteducimus · Answer

Is not the prob of both surviving 12/25?

Bunuel · Answer

12/25 is what you get if you assume  independence  (multiply 3/5 * 4/5).

But the problem never says the two groups’ survival outcomes are independent. Without that assumption, you have to consider all possible correlations. That’s why the solution gives a  range : the minimum consistent value is 2/5, and the maximum is 3/5.

So 12/25 is just one possible value inside that range, not the guaranteed answer.

At a wildlife sanctuary, researchers track the survival of two newly

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

MAX PROBABILITY	P(A)	P(NOT A)	TOTAL
P(B)	0.60	0.2	0.8
P(NOT B)	0	0.2	0.2
TOTAL	0.60	0.40	1

MIN PROBABILITY	P(A)	P(NOT A)	TOTAL
P(B)	0.40	0.4	0.8
P(NOT B)	0.2	0	0.2
TOTAL	0.60	0.40	1

GMAT Two-part Analysis (TPA) Questions

At a wildlife sanctuary, researchers track the survival of two newly

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards