Answer: 3/56
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Work Shown:
A = event of picking the "2" card
P(A) = probability of event A happening
P(A) = 1/8
This is because there is one card labeled "2" out of 8 cards total
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B = event of picking a number less than 6, given event A has happened
P(B) = 3/7
There are 3 cards less than 6 (those cards are labeled 3,4, and 5) out of 8-1 = 7 cards left over. We havent put the first card back so that's why 8 drops to 7. We also don't consider the "2" card. So that's where the 3/7 comes from.
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P(A and B) = P(A)*P(B)
P(A and B) = (1/8)*(3/7)
P(A and B) = (1*3)/(8*7)
P(A and B) = 3/56
