Question

A number is chosen from the set S = 1, 2, . . . , 1000. What is the probability that the chosen number is multiple of 2 and 3?

Answer 1

Answer:

0.166

Step-by-step explanation:

Answer :

We have integers 1, 2, 3,… 1000

∴ Total number of outcomes, n(S) = 1000

  The multiple of 2 and 3 both are 6,12,… 996.

Let m be the number of terms in above series.

∴ mth term = 996

 We know that,

am = a + (m – 1)d

Here, a = 6 and d = 6

Putting the value, we get

6 + (m – 1)6 = 996

⇒ 6 + 6m –6 = 996

⇒ m = 166  

= n(E)

P(E) = n(E) / n(S)

P(E) = 166 / 1000 = 0.166