## Interview Question

Data Scientist Interview

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# There are 50 cards of 5 different colors. It comprises of 10 Red cards, 10 blue cards, 10 orange cards, 10 green cards and 10 yellow cards. Each color will have the cards numbered between 1 to10. You pick 2 cards at random. What is the probability that they are not of same color and not of same number.

17

Easy. You need no formulas for this. Just some logic. Let's say we choose one card - Red number 9. Probability = (Available choices from leftover cards that do not violate constraint)/(Total cards left) We can not choose another Red card or number 9 of any other color = ( 0 red cards + 9 of each other color *4) / 49 = 36/49 = .73

Anonymous on

16

So here's the way I'm thinking about this one. We're drawing two cards and we want to make sure they're not the same number or same color. So the first card we draw can be anything (e.g. lets say, blue and number 5). It's the second card that we have to worry about... And for the second card, we're calculating the P(not blue and not 5). Because these two events aren't independent, P(not blue and not 5)=P(not blue)* P(not 5 | not blue). P(not blue) is 40/49. P(not 5 | not blue) is 36/40 because there are four 5's left, and we're only looking at the subset of cards that are not blue (40 cards). Therefore, the answer should be .734 (36/40 * 40/49)

Anonymous on

8

(1) choose 2 colors out of 5: C(5)(2)=10 (2) choose 1 number out of 10: C(10)(1)=10 (3) choose 1 number out of 9: C(9)(1)=9 (4) total combinations: C(50)(2)=1225 (5) probability: 10*10*9/1225=0.7347

choose 2 colors out of 5: C(5)(2)=10 on

4

let us say we picked one card: P(two cards have different color and numbers) = 1 - P(two cards have same color or same number) = 1 - # available choices / # total choices = 1 - (9 ( same color) + 4 (same number) )/49 = 1 -13/49 = 36/49

Vam on

1

Two cards with the same colors will never have the same numbers, and therefore the two events are exclusive. P(same number) = 4/49 and P(same color) = 9/49 P(not same number or not same color) = 1-4/49 - 9/49 = .734

Anonymous on

0

Two cards with the same colors will never have the same numbers, and therefore the two events are exclusive. P(same number) = 4/49 and P(same color) = 9/49 P(not same number or not same color) = 1-4/49 - 9/49 = .734

Anonymous on

1

Two cards with the same colors will never have the same numbers, and therefore the two events are exclusive. P(same number) = 4/49 and P(same color) = 9/49 P(not same number or not same color) = 1-4/49 - 9/49 = .734

Anonymous on