If the probability is 0.7 that event X will occur and 0.85 that event

Question

If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur?

(A) 0.15 
(B) 0.55 
(C) 0.595
(D) 0.7 
(E) 0.85

gmatophobia · Answer

We can use a Venn diagram to map the information.

Question : Minimum value of  p  ?

To minimize  p , we have to maximize  x .

The maximum value that  x  can take = 0.15

Minimum value of p = 0.7 - 0.15 = 0.55.

Option B

butter_chicken · Answer

Why can't we assume both events to be disjoint sets? that way P(XandY) = 0 and that's the minimum possilbe value.

Purnank · Answer

Question asked least value for X&Y
Therefore,
Union of both = 1
X + Y - X&Y = 1
0.7 + 0.85 - 1 = X&Y
X&Y = 0.55

Posted from my mobile device

ClaireCHEN · Answer

the least possible value of the probability that both events will occur = 1-(P of neither will happen)-(P of only one will happen),  quoting the graphic interpretation from gmatophobia  (which also inspired me for resolution!!!),  then p=1-n-x-y, since 2n+x+y=0.45, then p=n-0.45. P is the least when n is the biggest which is 1, so answer is 0.55

tombox · Answer

We can't assume that because we know that the sum of P(A) and P(B) is higher than 1.

The formula for probability of A OR B for disjoint sets is P(AorB)=P(A)+P(B) and as you might know a probability cannot be higher than 1.

The general formula (without assumption) is P(AorB)=P(A)+P(B)-P(AandB) so it becomes clear that P(AandB) cannot be = 0 in this case.

In fact, shifting the terms we get P(AandB)=P(A)+P(B)-P(AorB), we already have P(A) and P(B) so the only way to minimize the joint probability is to put P(AorB)=1 (the max value). This would give us 0.55.

Hope its clear.

Strategix · Answer

Concept similar to min-max overlap in Overlapping sets

Chance of occurrence of X = 70%
Chance of occurrence of X =85%

To minimize the overlap: X + Y - Total => 70%+85%-100% = 55%  (Option B) 
To maximize overlap: minimum value of the two i.e. X = 70%

If the probability is 0.7 that event X will occur and 0.85 that event

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If the probability is 0.7 that event X will occur and 0.85 that event

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