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Tickets numbered 1−10 are drawn at random and placed back in the pile. Find the probability that at least one ticket numbered 2-6 is drawn if there are 4 drawings that occur. Round your answer to two decimal places.

Answer :

FICHOHIN

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

  • Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

  • 5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

  • (1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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