Numbers are selected at random, one at a time, from the two digit numb

1.	Numbers are selected at random, one at a time, from the two digit numbers 00, 01, 02. . . 99 with replacement. An even E occurs if only if the product of the two digits of a selected numbers is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.
Answer» The given numbers are 00, 01, 02 . . . . 99. These are total 100 numbers, out of which the numbers, the product of whose digits is 18, are 29, 36, 63 and 92. ∴ p = P (E) = 4/100 = 1/25 ⇒ q = 1 – p = 24/25 From Binomial distribution P (E occurring at least 3 times) = P (E occurring 3 times) + P (E occurring 4 times) ⁴C₃p³q + ⁴C₄ p⁴ = 4 x (1/25)³ (24/25) + (1/25)⁴ = 97/(25)⁴

Numbers are selected at random, one at a time, from the two digit numbers 00, 01, 02. . . 99 with replacement. An even E occurs if only if the product of the two digits of a selected numbers is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.

Answer»

The given numbers are 00, 01, 02 . . . . 99. These are total 100 numbers, out of which the numbers, the product of whose digits is 18, are 29, 36, 63 and 92.

∴ p = P (E) = 4/100 = 1/25 ⇒ q = 1 – p = 24/25

From Binomial distribution

P (E occurring at least 3 times) = P (E occurring 3 times) + P (E occurring 4 times)

⁴C₃p³q + ⁴C₄ p⁴ = 4 x (1/25)³ (24/25) + (1/25)⁴ = 97/(25)⁴

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Numbers are selected at random, one at a time, from the two digit numbers 00, 01, 02. . . 99 with replacement. An even E occurs if only if the product of the two digits of a selected numbers is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.

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