I do not think we have to do serious math to answer this question. Both events happening vs any one event happening. B would be greater for obvious reason.

Both events happening = 0.5*0.4 = 0.2

any one event happening = 0.5+0.4 - 0.9

Please correct me on Math part if wrong.

So lets see Quantity A: Both get degree = \(P(tom) \times P(john)=0.5 *0.4=0.2\).

Quantity B: Atleast one degree gets awarded. We can write the following cases:

Tom gets a degree John doesnot = \(0.5 * (1-0.4)=0.3\)

John gets a degree Tom doesnot = \(0.4 * (1-0.5)=0.2\)

Both get a degree = \(0.4 *0.5=0.2\)

Total probability for quantity B is \(0.7\).

Hence B is greater.
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Answer: B
P(Tom passes) = 0.5
So, P(Tom Fails) = 1 - 0.5 = 0.5

P(John passes) = 0.4
So, P(Tom Fails) = 1 - 0.4 = 0.6

The two events are independent from each other.

A: P(Tom passes and John passes) = P(Tom passes) * P(John passes) = 0.5 * 0.4 = 0.2 [because events are independent, their intersection probability is multiplication of the individuals)

B: P(Tom passes and John passes) + P(Tom passes and John fails) + P(Tom fails and John passes) = 1 - P(Tom fails and John fails) = 1 - P(Tom fails)*P(John fails) = 1 - 0.5*0.6 = 1 - 0.3 = 0.7
So B is bigger than A.
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