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you pick a number at random. without putting the first card back you pick a second card at random 4 5 6 what is the probability of picking a 6 then picking a number greater than 5 in percentage ?

User CrouZ
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1 Answer

1 vote

Explanation:

if I understand correctly we have only 3 cards to pick from : 4, 5, 6

my answer bases on that understanding.

we don't need any formal calculation, just common sense :

if the first picked card is the 6 card, and we don't put it back, there is no card left greater than 5 for the second pick.

so, this is an impossible event with the automatic probabilty of 0 or 0%.

formally, this looks like this :

a probability is always the ratio

desired cases / totally possible cases.

100% corresponds to 1 (the sure event = the sum of all possible outcomes). so, the % is always 100 times the actual probability.

to pick the 6 out of the possible 3 cards the probability is

1/3 = 0.333333... = 33.3333...%

one desired card out of the possible 3.

now, we don't put that card back.

we are left with 2 cards : 4, 5

the probability to pull a card greater than 5 out of these 2 cards is

0/2 = 0

0 desired cards out of the possible 2.

the probabilty of this combined event of these 2 (independent !) single events is the multiplication of the individual probabilities :

1/3 × 0/2 = 0/6 = 0 = 0×100% = 0%

User Evengard
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