There are 15 tickets in a box, each bearing one of the numbers from 1

1.	There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn: i. shows an even number. ii. shows a number which is a multiple of 5.
Answer» Sample space, S = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} ∴ n(S) = 15 i. Let A be the event that the ticket drawn shows an even number. ∴ A = {2, 4, 6, 8, 10, 12, 14} ∴ n(A) = 7 ∴ P(A) = \(\frac{n(A)}{n(S)}\) ∴ P(A) = 7/15 ii. Let B be the event that the ticket drawn shows a number which is a multiple of 5. ∴ B = {5, 10, 15} ∴ n(B) = 3 ∴ P(B) = \(\frac{n(B)}{n(S)}\)= 3/15 ∴ P(B) = 1/5 ∴ P(A) = 7/15 ; P(B) = 1/5

There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn: i. shows an even number. ii. shows a number which is a multiple of 5.

Answer»

Sample space,

S = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15}

∴ n(S) = 15

i. Let A be the event that the ticket drawn shows an even number.

∴ A = {2, 4, 6, 8, 10, 12, 14}

∴ n(A) = 7

∴ P(A) = \(\frac{n(A)}{n(S)}\)

∴ P(A) = 7/15

ii. Let B be the event that the ticket drawn shows a number which is a multiple of 5.

∴ B = {5, 10, 15}

∴ n(B) = 3

∴ P(B) = \(\frac{n(B)}{n(S)}\)= 3/15

∴ P(B) = 1/5

∴ P(A) = 7/15 ; P(B) = 1/5

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There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn: i. shows an even number. ii. shows a number which is a multiple of 5.

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