Question

# Wardrobe of Samuel has 5 pairs of socks, 7 pairs of shoes and 10 shirts. If Samuel picks an item at random, what is the probability that the picked item is a shirt? (Consider a pair of socks or shoes as one item)

A
1011
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B
511
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C
611
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D
522
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Solution

## The correct option is B 511 Given: ∙ Number of pairs of socks =5 ∙ Number of pairs of shoes =7 ∙ Number of shirts =10 Total number of items available in Samuel's wardrobe = Number of pairs of socks + Number of pairs of shoes + Number of shirts =5+7+10 =22 Let P(Shirt) denotes the probability that the picked item is a shirt. Number of favorable outcomes = Number of shirts = 10C1 Number of possible outcomes = Total number of items available in Samuel's wardrobe = 22C1 P(Shirt)=Number of shirtsTotal number of items available in Samuel's wardrobe P(Shirt)= 10C1 22C1 P(Shirt)=1022 P(Shirt)=511 The probability that the picked item is a shirt is 511. Therefore, option (b.) is the correct answer.

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